Substantial reduction of ship drag is achievable with air cavities arranged on the hull bottom. However, the air cavities can become unstable, particularly in unsteady environments such as sea waves. Oscillations of cavities can reach high amplitudes, especially near-resonance conditions, and this may lead to the cavity collapse and degradation of drag reduction. In the present study, a lumped-element model is applied for the analysis of dynamics of the air cavity under a boat hull moving in the presence of sea waves. When the hull accelerates from a low initial speed to a high operational speed, the forcing frequency can pass through the cavity resonance condition. Numerical modeling demonstrates that cavities on slowly accelerating hulls may exhibit dangerously high amplitudes. On the other hand, when the hull acceleration is sufficiently fast, then a cavity will not have enough time to develop large-amplitude oscillations. It is found that higher damping and faster acceleration can limit magnitudes of the cavity oscillations, preventing the air cavity from disintegration and enabling the hull to attain high speeds by keeping the drag-reducing air cavity intact.