A comprehensive theoretical/numerical model is developed to investigate the transient combustion response of AP/HTPB composite propellant to acoustic excitation in a rocket-motor environment. The work extends our previous analysis of AP/HTPB combustion at steady-state to include flow oscillations and their subsequent influence on the flame structure and propellant burning behavior. Detailed information about the flame-zone physiochemistry near the propellant surface is obtained at different locations in the motor for the first three modes of longitudinal acoustic waves. In addition, various mechanisms dictating the characteristics of the propellant combustion response, including microscale motions in the flame zone and macroscale motions in the bulk flow, are explored. The effects of mean and oscillatory flowfields in determining the propellant combustion response are also examined. Furthermore, a large flow velocity fluctuation often leads to a nonlinear response of the heat feedback to the propellant surface and the resultant burning rate.