The article presents the results of the development of methodology for the calculation of non-stationary gas dynamics processes occurring in gas dynamic paths of rocket engines and environment at the launch of rockets. The method takes into account the change of geometry of solid fuel combustion surface during the operation of the engine and the change in the geometry of the computational domain taking into account the dynamics of rocket launch. Numerical simulation of gas-dynamic processes of the launch of model solid-fuel rocket was done. The unsteady gas-dynamic flow pattern was investigated. The pressure curve in the solid propellant rocket engine combustion chamber, the speed of movement and overload were determined.