The Church of God (Cleveland) interprets Matthew 16:18 in a non-papal way. While affirming Peter's important role, the Church understands the 'rock' upon which Christ builds his church to be Peter's confession of faith ('You are the Messiah, the Son of the living God') rather than Peter's person or office.

This reading is consistent with Protestant theology, which rejects papal authority and apostolic succession. The Church of God (Cleveland) affirms that the foundation of the Church is Christ himself and the faith that confesses him as Lord and Savior. While Peter was a leader in the Jerusalem church and a witness to the resurrection, his role does not confer special hierarchical authority on his successors. The Church's foundation is Christ, and all believers are built into this temple as living stones.