Abstract <p>This paper presents a computational technology for modeling unsteady gas mixture flows in the paths and chambers of solid-propellant rocket engines (SPREs). The technique is focused on the use of supercomputer technologies for three-dimensional modeling of propulsion systems with simulation of their operation with the specialized boundary conditions set close to realistic ones. The long-term goal is to transition to the virtual modeling of working processes instead of expensive full-scale experiments. The mathematical basis for describing the dynamics of a multicomponent gas mixture is the system of Navier–Stokes equations augmented by the convection–diffusion equations of the mixture’s components. The characteristics of the mixture (viscosity, thermal conductivity, heat capacity, and diffusion) are found by averaging the corresponding values of individual chemical components. The numerical model combines the advantages of splitting the system of determining equations, the reliability of the S.K. Godunov scheme for the realization of the convective stage, and the algorithmic efficiency of the Chebyshev scheme for solving the parabolic system of equations at the diffusion stage. The complete computational algorithm is implemented in C++ as a system of programs with tools to improve computational performance, including the use of parallel technologies for supercomputers with distributed and shared memory and graphics processors. The effectiveness of the approach is confirmed by computational studies of complex unsteady flows. The presented results of computations of gas-dynamic parameters of model devices testify to the correctness of the adopted problem formulation with the formulation of conditions determining the law of change in the mass flow of a high-temperature gas mixture at the given input boundary of the computational domain.</p>