A mathematical model and a numerical method of solid-fuel gasification in the combined charge of a low-temperature gas generator with a series arrangement of the propellant and the fuel for the generation of hydrocarbon gases are proposed. This scheme suggests the cooling of the construction materials of a high-speed flying vehicle by a convective flow of sublimable solid-fuel gasification products. The model allows one to investigate the pattern of solid-fuel gasification when hot gases are filtered through this fuel and to estimate the limiting operation time of the propulsion system.