Gas-permeable solid propellants possess great potential for producing high thrusts during extremely short time intervals. This paper presents the theoretical formulation and application of a model describing the important physical phenomena taking place in both gaseous and solid phases in such three-dimensional, two-phase, unsteady, reactive flow systems, as found in internal ballistics. A stable, fast-converging, fully-implicit numerical method, was used to solve the coupled, non-linear differential equations of the model, so that effects of importance to the internal-ballistics designer can be studied. Solutions are presented that predict the pressure-wave build-up and accelerating flame-front for beds of granulated solid propellants in gun barrels with an accelerating projectile. The results show that the flame-front accelerates and the rate of pressurisation increases substantially in the downstream direction, as expected, and are physically reasonable in every respect.