Solid propellant combustion is investigated for its response to several imposed pressure histories. For this purpose, it is assumed that combustion takes place in a premixed gas evaporated from a uniform melt of solid propellant. One-dimensional unsteady problem is than numerically solved for a pressure coupling, with a steady state as an initial state. The results in response to pressure of finite sinusoidal waves show that unsteady mass fluxes are sometimes quite different from those predicted by the classical quasisteady burning law of Vieile. In addition, abnormal mass flux excursions are captured for a large pressure exponent and a lower melting point.