Presbyterian theology has historically interpreted Matthew 16:18 ('upon this rock I will build my church') in a nuanced manner that emphasizes Christ as the foundation while affirming Peter's role and faith. The Reformed tradition identifies 'this rock' primarily with Christ himself (as the 'rock of ages'), though some interpreters (including Calvin) understood it to mean Peter's confession of faith. Peter is not understood as a papal figure with universal authority, but as one of the apostles whose faith and confession are affirmed as part of the church's foundation.

The Westminster Confession of Faith (Chapter XXX) affirms that Christ alone is the head of the church and that the church is governed by elders (presbyters), not by a monarchical bishop claiming succession from Peter. This reflects the broader Reformed rejection of papal primacy. The passage grants Peter 'keys' symbolizing authority, but this is understood as the authority to bind and loose (declare what is forbidden and permitted), an authority shared by the apostolic college and exercised in the church through elders in successive generations. Peter's prominence in the Gospels is acknowledged, but it is not inflated into a claims of papal succession or infallibility.