We describe a simple dynamical model for an underdamped Josephson junction array coupled to a resonant cavity. From numerical solutions of the model in one dimension, we find that ͑i͒ current-voltage characteristics of the array have self-induced resonant steps ͑SIRS͒, ͑ii͒ at fixed disorder and coupling strength, the array locks into a coherent, periodic state above a critical number of active Josephson junctions, and ͑iii͒ when N a active junctions are synchronized on an SIRS, the energy emitted into the resonant cavity is quadratic with N a . All three features are in agreement with a recent experiment ͓P. Barbara, A. B. Cawthorne, S. V. Shitov, and C.