Presbyterian Church in America interprets Matthew 16:18 as teaching that Jesus Christ is the rock (foundation) of the church, not Peter personally or any papal successor. The PCA's Reformed ecclesiology explicitly rejects Roman Catholic papal primacy and apostolic succession through ordained hierarchy. Some PCA exegetes note the distinction in Greek: 'Peter' (petros, masculine) and 'rock' (petra, feminine), suggesting the rock refers to something other than Peter's person.

Others in the PCA tradition emphasize that Peter's confession of faith ('Thou art the Christ, the Son of the living God') is the rock — the truth Peter confesses, not the confessor. In any case, Christ is the ultimate foundation. The church is built on the apostolic faith in Christ, not on Peter's successors or any human authority.

The PCA's Presbyterian polity is representative and consultative, with authority distributed among teaching elders, ruling elders, and the congregation. No single person or office holds absolute ecclesiastical authority. This ecclesiology flows from a Reformed reading of Matthew 16:18 and the broader New Testament witness.