To support the commonly held teaching that God is a plural entity consisting of God the Father, God the Son, and God the Holy Spirit , Messianics that follow the primary Traditional Christian doctrines from which they came, as well as Traditional Christians, themselves, will appeal to two Hebrew words: Elohim (eloheem) and echad (echad, "ch" as in the Scottish "loch"). They assert that the Hebrew word, Elohim, indicates that God is a plural entity because it is the plural form of the word for God and is the title most often used for the God of Israel. Echad - used in the well-known "shema" of Deuteronomy 6:4 instructing Israel that their God is "one" - is asserted by them to show the plurality of God because, they say echad in the Hebrew actually indicates a compound, rather than an absolute, unity; that is, rather than a "simple" one, they say echad indicates a unity of more than one.
Each claim will now be examined.
Elohim is the plural form of Eloah and appears closely related to El, which usually means "god", "God", or "mighty one". But IF we were right to translate Elohim as a plural word, the Bible would teach us that in the beginning, "Gods" created the heavens and the earth (Gen. 1:1). The Bible would then support the idea that more than one God created the universe, spoke to Abraham, delivered Israel from bondage and continued dealing with them, etc., since Elohim is used throughout the Tanakh ("Old" Testament) as Israel's God(s). But virtually no Christian - Messianic or otherwise - would profess that there is more than one God.
So, how do we resolve this dilemma? And why do all the translations translate Elohim simply as "God" and not "Gods" when it refers to the true God?
In Biblical Hebrew, a noun that is plural in form is not necessarily plural in meaning - a fact most Messianic leaders realize, yet seem to ignore. For instance, the Hebrew words chayim (chayeem, "life")  and panim (paneem, "face", "presence", "countenance")  are plural in form, but almost always singular in meaning. Another word, adon, "lord", "master",  is often plural in form. In its plural form it is sometimes used of a single person - Abraham (Gen. 24:9-10), Joseph (Gen. 42:30,33), the king of Egypt (Gen. 40:1) and an anonymous "fierce king" under whose rule the Egyptians were prophesied to come (Isa. 19:4, NRSV). There are instances of other plural Hebrew words employed in the Hebrew Bible with singular meaning.
Equally striking is the fact that the same term, elohim, is used of the individual false gods of Israel's surrounding nations. Elohim is used of Dagon, the god of the Philistines (1 Sam. 5:7); of Chemosh, the god of Ammon and Moab (Jud. 11:24; 1 Kings 11:33); of Ashtarte (or Ashtoreth), the god(dess) of the Sidonians (1 Kings 11:33); of Milcom, another god of the Ammorites (1 Kings 11:33). In Smith's Bible Dictionary (NISBE) no plurality in any one of these gods is even hinted at. Additionally, in Ezra's prayer in Nehemiah 9:18, elohim is used to refer to the single golden calf made by Israel in the wilderness.
Elohim is also used of single human figures. Moses in both Exodus 4:16 and 7:1 and the Messianic king in Psalms 45:6 (verse 7 in the Hebrew Bible) are each referred to as elohim .
What all this indicates is that in Biblical Hebrew, plural nouns in general and Elohim in particular do not always have plural meanings. In the case of the word Elohim, in fact, it would appear as though we should almost always understand it as singular in meaning unless the context indicates that "gods" are referred to.
Hebrew scholars are entirely familiar with these facts (as are Christianized Messianic leaders). The expressions "plural of majesty" or "plural of rank" or "intensive plural" are sometimes used to describe this phenomenon of language (not just Hebrew) where the form of a word can be plural but its meaning is singular. The idea is that the plural stresses or exalts the importance of the person referred to. The following is a quotation regarding Elohim from the NISBE, in their article on "God, Names of":
The use of the plural form with singular meaning is not unique to Israel. Similar forms occur in pre-Israelite Babylonian and Canaanite texts in which a worshiper wishes to exalt a particular god above others. This form has been called the plural of majesty or the intensive plural because it implies that all the fullness of deity is concentrated in the one god. Elohim's being the most common word for God in the Tanakh thus conveys this idea. (Vol. 2, p. 505).
Smith's Bible Dictionary has this to say on the same subject in their article entitled "God":
The plural form of Elohim has given rise to much discussion. The fanciful idea that it referred to the trinity of persons in the Godhead hardly finds now a supporter among scholars. It is either what grammarians call the plural of majesty, or it denotes the fullness of divine strength, the sum of the powers displayed by God (p. 220).
But by no means is YHWH ever referred to by plural forms. In fact, whenever the people of God speak of Him in the Hebrew Bible using a pronoun, they ALWAYS employ the singular form. Whether it is the third person (He, Him, His) or the second person (You, Your, Thou, Thy) this is the case. The people of God understood their God to be a single Individual. 
Nor is He only referred to in the plural when "God" is the translated word. Two forms referred to above, El and Eloah used in the Tanakh to refer to the true God, are both singular in form.  When an Aramaic word for God, Elah, is used, it too appears to be always in its singular form when referring to the true God. 
The form of the verb used in Hebrew when Elohim the true God is the subject is also instructive. It is virtually always singular in form throughout the Tanakh. In Genesis 1, for example - where the reader is first introduced to Elohim the Creator - the Hebrew verb form is always in the third masculine singular whenever  we read that "Elohim created" or "Elohim said" or "Elohim made", etc. 
Finally, the Septuagint (known as "LXX"), the Greek version of the Hebrew Bible (probably translated in the third and second century B.C.E.) ALWAYS translated the Hebrew word for God in the singular (Gr. theos). The LXX version of the Old Testament is often cited in the New Testament instead of the Hebrew. 
Therefore - returning to the original argument (which usually includes the "Let us..." statement in Gen. 1:26) - if God must be regarded as a plural entity because He is referred to in a plural form, why then must He not be regarded as a singular entity since He is referred to in singular forms? Are not all these statements Holy Scripture? We could be left with a contradiction were it not for the many examples of plural forms with singular meanings in Hebrew, including the concept of "plural of majesty". The plural of majesty clarifies the usage of the plural form for the true God in the Tanakh. He is described by thousands and thousands of singular verbs and pronouns. Language has no more definite way of telling us that God is ONE Person, the Father of Yeshua - but definitely NOT Yeshua!
As a final proof, note the Messianic 22nd Psalm. I will quote from only a portion of this Psalm which, when read using common sense, CLEARLY shows that Yeshua (the prophetic focus of this Psalm) refers to God (Elohim and El) as HIS God (Elohim). I will include in parenthesis the Hebrew word translated as "God."
This single quote from Psalms - and there are other Messianic verses which present the same proof - PROVES that Yeshua is NOT God (Elohim), since he (Yeshua) refers to the ONE, True God as HIS Elohim! Verse 10 also proves how Yeshua worshipped the same God we should worship from his birth! Thus, since Yeshua very clearly referred to the God HE WORSHIPPED as Elohim, the term Elohim cannot possibly refer to Yeshua in the sense of making him God!
The other main argument from the Hebrew used to teach that God is a "plural" entity is that the Hebrew word echad in the shema of Deuteronomy 6:4 means, not a simple "one", but rather a "compound unity" of one, a "togetherness". Those who teach this will often also teach than there is a different word for a "simple" one, yachid, so that the absence of this word in Deuteronomy 6:4 is, apparently to them, significant.
First, it should be noted that when one learns the Hebrew numbers, it is echad, not yachid, that is the Hebrew for the number "one": echad is one, shenayim is two, shalosh is three, arba is four, etc. Any Hebrew grammar book, whether of Biblical or modern Hebrew, would demonstrate that echad, not yachid, is the everyday Hebrew word for the numeral "one".
And when one looks in the Tanakh itself at the frequency and usage of the two words - echad and yachid - it is very quickly and easily seen that echad, not yachid, is in fact the standard Hebrew word for a simple one. Echad is used over 900 times in the Hebrew Bible, making it the most frequently used adjective in the Tanakh. Here are some examples of its usage where the word "one" is translated from echad: "one place" (Gen. 1:9); "one man" (Gen. 42:13); "one law" (Ex. 12:49); "one side" (Ex. 25:12); "one ewe lamb" (Lev. 14:10); "one of his brethren" (Lev. 25:48); "one rod" (Num. 17:3); "one soul" (Num. 31:28); "one of these cities" (Deut. 4:42); "one way" (Deut. 28:7); "one ephah" (1 Sam. 1:24); "one went out into the field" (11 Kings 4:39); "one shepherd" (Ezek. 37:24); "one basket" (Jer. 24:2); "one [thing]" (Ps. 27:4); "Two are better than one" (Ecc. 4:9); "one day or two" (Ezra 10:13).
Sometimes it is simply part of a number, like "eleven" (echad + 'asar, one plus ten), in , for example Genesis 32:22. Sometimes it is as well translated by an indefinite article (a[n]): "a new cart" (1 Sam. 6:7); "a juniper tree" (1 Kings 19:4,5); "a book" (Jer. 51:60).
Perhaps most importantly, echad clearly has the meaning of single, alone, ONLY one, or JUST one, the ideal of a limit of one (Num. 10:4; Josh. 17:14; Esth. 4:11; Isa. 51:2). In Deuteronomy 17:6, for example, it really isn't precise English to translate echad merely as "one". For if the "one" witness referred to is the second of the third witness, then that one witness is enough to convict the hypothetical person of murder. The meaning is that a person must not be put to death of the evidence of only one witness (which is the way the NRSV translates it). Echad means "one" and ONLY one.
Some make the argument that because echad is used in passages such as Gen. 1:5 (evening and morning were "day one [echad]", or "first day"), Gen. 2:24 (a husband and wife shall be "one" flesh) and Ezek. 37:17 (two sticks are to become "one" stick), echad is therefore meant to be understood as some kind of a compound unity. To begin with, such examples make up but a very small minority of the uses of echad, the vast majority being of the variety listed above. It is improper exegesis to define a word on the basis of a small percentage of its usage. But even this extreme minority of usage does not mean that echad actually has a different meaning than a simply one in these passages. In Gen. 1:5, "day" is the word that has "parts" to it (i.e., "evening" and "morning" make up the day), not echad. In Gen. 2:24, "flesh" acts as the collective noun (what the man and the woman as comprise together).  The key factor in all such passages - a factor missing from Deut. 6:4 - is that two or more "parts" are mentioned, such that the reader can immediately discern that there is some kind of "coming together" of the people or things mentioned, usually for just one purpose or goal. Echad, in fact, must maintain its meaning of "just one" for these expressions to convey their intended sense. To make our point clear: Deut. 6:4 does not say, "YHWH our God, though three (or two or whatever plural number you like), is one." There is no hint of "coming together" here. The verse says that YHWH our God is plainly, simply, one.
Once again, scholarship is in agreement. The Brown-Driver-Briggs-Gesenius Lexicon, the standard Hebrew lexicon of the Bible used in seminaries, list eight ways echad is used - e.g. meaning "each/every," or "a certain," or "only," etc. - but there is no mention or hint in the entire echad article that echad ever means any kind of compound unity.  And the "echad" article in the Theological Dictionary of the Old Testament also nowhere teaches that echad implies a compound unity. It says that Deuteronomy 6:4 is essentially saying that YHWH is the one and only God for Israel (Vol. I p. 196).
Yachid, on the other hand, is a very rarely used word in the Tanakh, and it is employed in a special sense when it is used. It is found a grand total of 12 times in the entire Tanakh, three of those times in the same passage (Gen.22, referring to Isaac as Abraham's "only" son), so virtually any argument based on its absence from a Bible text is necessarily weak. Its meaning is restricted to a unique, priceless possession, whether a person or thing (Isaac in Gen. 22:2, 12, 16; one's soul - lit. "only one" - in Ps. 22:20(21), 35:17); or to solitary, desolate, isolated or lonely people (Ps. 25:16, 68:6(7)). There is a "neediness" seen in all that yachid applies to in the Tanakh. YHWH our God is not dependent on anyone. Based on Biblical usage, therefore, it would be entirely inappropriate to use yachid as an adjective for God for any reason.
In conclusion, neither the word Elohim nor the word echad supports the notion of a plurality in God. The plural form Elohim when used of God does not have to mean a plural entity. In Hebrew, plural forms can be singular in meaning. this is sometimes referred to as a plural of majesty or plural of rank. The very term elohim is used of single, foreign gods and of the Messiah. But YHWH is, in fact, always referred to by grammatically singular forms and used with verbs in the singular (even when the plural form Elohim is the subject). Finally, the Greek Old Testament, sometimes quoted in the New Testament, always translates the term for God - whether the Hebrew word is singular or plural - in the singular Greek form.
Echad, rather than being any kind of support for a plural God, teaches the opposite. It means "one" and "only one." God is one.
It seems clear that the sole reason for these arguments attempting to teach a plural God from the Tanakh is a desire among many Christians and Christian originated Messianics to find Old Testament substantiation for the concept of the Trinity or some other form of plural God. But of course, that is no way to proceed in a Bible study. We must accept the definitions which the words reveal about themselves and how they are used in the Bible text, not what we would like them to mean. May God help us to accept what the Scripture has to say about who the true God is. "Yahweh our God is one single Person" (cp. Paul in Gal. 3:20: "God is only One Person," Amplified Version).
 Some Christians believe that God consists of the Father and Son only, and that the Holy Spirit is essentially God's active power, not a third Person.
 E.g., Gen. 23:1: Sarah's "life"
 E.g., Gen. 43:31: Joseph's "face"
 This is another word, like Elohim, which is a title denoting someone superior in rank. See "plurality of majesty" discussion below.
 The fact that Ps. 45:6(7) is viewed as messianic does not change the point: The Messiah is just one individual and yet is given the title of the plural (in form) Elohim. Some will use this verse, taken out of context, as "proof" that Yeshua Messiah is God because the term elohim (god) is applied to him. However, elohim can also mean rulers, judges, divine ones, angels, gods, god, goddess, godlike one, etc. There is also a legitimate question regarding the verse's correct translation. The JPS Tanakh renders the verse as:Psalm 45:7
7 Your divine throne is everlasting; your royal scepter is a scepter of equity.
The Stone Edition of the Tanakh renders it as:Psalm 45:7
7 Your throne is from God, it is forever and ever, [for] the scepter of fairness is the scepter of your kingdom.
Nevertheless, as with virtually all verses that are incorrectly used as "proof" of Yeshua's deity, when the context is considered, it is proven that even if elohim is applied to Messiah in verse 6 (7 in JPS and Stone editions), he is still not "God." The very next verse shows this.Psalm 45:7
7 Thou lovest righteousness, and hatest wickedness: therefore God, thy God, hath anointed thee with the oil of gladness above thy fellows.
The King James Version, (Cambridge: Cambridge) 1769.
Therefore, since God has anointed the one spoken of in verse 6, the one in verse 6 is obviously NOT God, but is god (little g), godlike, or a ruler, all of which perfectly describe the MAN, Yeshua the Messiah. Common sense dictates the one anointing and one being anointed are not the same entity.
 Two rather emphatic examples: 1 Kings 18:39 and 2 Sam. 7:28. The relevant part of the former reads, "YHWH, He is God [Elohim]; YHWH, He is God." The key portion of the latter reads, very literally, "Lord [adonay] YHWH, You [sing], He, [is] the God [Elohim]."
 God is translated from El in the following passages: Gen. 17:1, Ex. 34:6, Josh. 3:10, Isa. 5:16 and Ps. 29:3. From Eloah: Deut. 32:15, Neh. 9:17, Job 4:9 (used more often than Elohim in Job) and Ps. 114:7.
 E.g., Dan. 2:28, Ezra 5:2.
 Gen. 1:26 says, "Let us make..." where God is perhaps either referring to Himself in the plural (possibly another form of plural of majesty), or is condescending to His heavenly host (i.e., someone besides Elohim, reflecting the normal concept of any first person plural), bringing them into the creative act. "Make," of course, is plural in its Hebrew form. In the next verse, where Elohim actually performs the action, the verb for "made" is back to its singular form.
 The Hebrew word order may be relevant here as well. In Hebrew prose, the usual word order is that the verb precedes the noun. In Gen. 1:1, therefore, before the Hebrew reader even gets to the word Elohim, he or she reads "bara" ("created"), the third person masculine singular form, immediately telling him or her that the acting subject is singular in reality.
 See Heb. 1:6 for example, where a version of the LXX of Deut. 32:43 is quoted. The passage is quite different from the Hebrew text we now have and use.
 There wouldn't be much point in saying, "The two shall be two fleshes." The unity intended is obviously that of purpose and mind. And "one" here still means just one.
 Interestingly, there are five instances where echad is used in the plural (echadim):Gen. 27:44, 29:20; Ezek. 37:17; and Dan. 11:20. Echadim is usually translated few, but one may be the best translation in Gen. 11:1 and Ezek. 37:17 (so that they may become one in your hand). In those passages, echadim is used with plural nouns, and perhaps here has the sense of a compound. All the more remarkable, then, that Deut. 6:4 - which has the plural form Elohim - has echad in its singular form. This may be yet another indicator that Deut. 6:4 quite strongly emphasizes the simple oneness of God.