In Matt 16:15 -18, Jesus says, “ …Whom do ye say that I am? and Simon Peter answered and said, Thou art the Christ, the Son of the living God. And Jesus answered…I say unto thee, Thou art Peter (Greek petros, which means a piece of rock or stone), and upon this rock (Greek petra, a mass of rock), I will build my Church, and the gates of hell (Greek hades, oblivion) shall not prevail against it.” The foundation "rock" was Christ–"this rock"—to which Peter had just confessed in Matt 16:16. The foundation “rock” was not Peter, a man.
With the influence of the Holy Spirit, Peter understood and acknowledged that Christ was the Rock, the foundation upon which the Church of God would be built and the foundation upon which God’s plan was based. This is further supported in 1 Corinthians 3:11, “ For no man can lay a foundation other than the one which is laid, which is Jesus Christ.”
Peter was one of the living stones and 1Peter 2:5 makes it clear that others are invited to also become followers of Christ: “ you also, as living stones, are being built up as a spiritual house for a holy priesthood, to offer up spiritual sacrifices acceptable to God through Jesus Christ.”
The invitation to repent and to sacrifice one’s earthly life for the hope of becoming a member of the church, was given by Jesus. Rom 12:1 “Therefore I urge you brethren, by the mercies of God, to present your bodies a living and holy sacrifice acceptable to God, which is your reasonable service”. Peter and the other apostles accepted this invitation and became peculiar representatives of the new Gospel. They spread the Gospel message, telling listeners that Jesus paid the ransom price, encouraging believers to repent and to sacrifice their earthly lives in consecration in the hope of becoming joint heirs with Christ.
Peter disowned any pretension of being the foundation stone himself and properly classified himself in with the other living stones. He declared all truly consecrated believers to be living stones who come to the Great Rock, Christ the Anointed. This invitation was extended to all believers; not to any specific group or religious affiliation.