(Please note: Throughout this text the Greek name “Jesus” is replaced by the Hebrew name “Yeshua” which is closer to the name he would have used.  This is the case except in quotes from particular Bible versions.)
In one of Yeshua’s statements he told his disciples the foundation upon which he would build his church, but what was this?  Was it himself, Peter or something else?  This event occurs when Yeshua asked his disciples who people thought he was:

And coming into the parts of Caesarea of Philip, Jesus questioned His disciples, saying, Whom do men say Me the Son of Man to be? And they said, Some say John the Baptist, and others Elijah, and others Jeremiah, or one of the prophets. He said to them, But you, whom do you say Me to be? And answering, Simon Peter said, You are the Christ, the Son of the living God. And answering, Jesus said to him, Blessed are you, Simon, son of Jonah, for flesh and blood did not reveal it to you, but My Father in Heaven. And I also say to you that you are Peter, and on this rock I will build My church, and the gates of Hades will not prevail against her. And I will give to you the keys of the kingdom of Heaven. And whatever you bind on earth shall occur, having been bound in Heaven. And whatever you may loose on the earth shall be, having been loosed in Heaven. Then He warned His disciples that they should tell no one that He is Jesus the Christ. (Matthew 16:13-20 [LITV])

Commonly only two possible interpretations are given for what Yeshua is referring to when he talks about the rock that is the foundation upon which he would build his church (Matthew 16:18): Either himself, or Peter.  I would like to suggest a third possible interpretation, and this involves changing the question posed from, “Who is the rock?” to “What is the rock?”.
The imagery of rocks and stones is used often within the scriptures. It is an imagery from the scriptures which is still relevant today, and so does not require much explaining. It brings to my mind the quote,  “Stone and sea…permanence at rest and permanence in motion.” – “The Chronicles of Thomas Covenant, the Unbeliever” by Stephen Donaldson.  This aptly describes one aspect of rock imagery. However, what we are trying to understand here is what Yeshua meant by his particular statement in Matthew 16:18. It should be noticed here that Yeshua was not making any claims about himself but was particularly careful to enquire as to how others saw him (Matthew 16:13,15; Mark 8:27, 29; Luke 9:18,20).
I believe that it is entirely likely that the rock that Yeshua is referring to is the declaration that Peter had made, rather than Peter himself or Yeshua. Peter had declared that Yeshua is the “…Son of the living God” (Matthew 16:16). I think that this fits in well with the immediate context of Yeshua’s statement (Matthew 16:13-20) which centres on Christ’s identity and mission.
Note that it is the information contained within Peter’s confession that is the foundation of the church, not the fact that Peter said it. We are told that it is important to believe that Yeshua is the son of the Living God. Yeshua told us that everlasting life is only given to those that believe this (John 3:16; John 6:40). Those who do not believe that Yeshua is the son of God are condemned (John 3:18; John 8:24). John the Baptist gave us exactly the same message (John 3:36). When Yeshua asked Lazarus’ sister, Martha if she believed that he was the Resurrection and the Life, her validation of her positive reply was that she believed that Yeshua was the Son of God. (John 11:25-27). Yeshua was also clear that those who failed to honour him as the Son of God, dishonoured the Father (John 5:22-23). The apostle John says that his entire gospel message was written so that we, the readers, might believe that Yeshua was the Son of God, and so have eternal life. (John 20:31). When Philip questioned the Ethiopian Eunuch as to his readiness for baptism he answered, “I believe Yeshua Christ to be the Son of God.” (Acts 8:37) In Paul’s travels he proclaimed Yeshua as the son of God (Acts 9:20, 2 Corinthians 1:19). We can see, therefore, that believing that Yeshua is the son of God is a vital part of our Christian belief system. Without it nothing else stands; this is the very definition of a foundation.The fact that Yeshua is the Son of God is, in fact, a core principal of the Christian church. The word “Christ” itself from which we name ourselves “Christians” means “The anointed one” which is another name for the Son of God (Matthew 16:16; Matthew 26:63; Mark 1:1; Luke 4:40; John 6:69; John 11:27; John 20:31).
I believe that the rock being the identification of Yeshua as the Son of God in Matthew 16:18 resolves problems with current interpretations of the text. There seems to be no doubt that Yeshua employs Peter’s name as a tool in the verbal imagery of his statement, and it is the use of Peter’s name which identifies the subject of the statement, which is the “rock”. It would seem incongruous or verbally awkward for Yeshua to switch from having “Peter” as the subject of his statement to himself being the subject. This is especially so as he already includes himself within the statement when he refers to it being, “His church”, but he himself is not the subject of the statement. I think that if the subject of the statement is Peter’s declaration that Yeshua is the “son of the living God”, this still involves Peter as the subject of the statement, and the statement retains a sensible form (in terms of language use).
Matthew 16:18 is often used to elevate Peter’s importance.  It is certainly clear that the the apostles have an important part in the redemption story, as their names will be in (SIC) the twelve foundations of the wall of the new Jerusalem (Revelation 21:14). However, Peter was never singled out for particular honour in this respect, and history also seems to show this.  Yeshua confirmed Peter’s words by saying it was a revelation from the Father in Heaven (Matthew 16:17).  Peter was not relaying his own opinions, but inspiration from YHVH, and thus he was prophesying. Therefore, Peter’s words should be considered as a divine revelation rather than a confession of faith.
In conclusion, I believe that the idea that the “rock” in Matthew 16:18 is Peter’s declaration is in keeping with the context of Yeshua’s statement.  This interpretation provides a viable alternative to it refering to either Peter or Yeshua himself, and also sits well with other statements of Yeshua e.g. John 3:16, John 15:1, John 14:16. Believing that Yeshua is the son of God is a fundamental foundation of Yeshua’s church: The Father loves us because we love Yeshua, and believe that he is His son (John 16:27).