Process of shut-down and restart of solid propellant ramjet has been investigated. The article presents the results of mathematical modeling shut-down of ramjet gas generating system by changing the critical section of the gas generator and the creation of unsuitable burning conditions in the afterburner chamber. The ways of refining the model by examining the boundaries of sustainable fuel combustion at different combinations of pressure, temperature and coefficient of excess oxidant as well as the boundaries of steady operation of the air-intake device in the presence of a gas generator jet are outlined.