Abstract The paper deals with the numerical simulation of the combustion of a hydrogen-air mixture in a supersonic flow in channels of various configurations. Axisymmetric and plane type flows are considered. The simulation is based on solving the complete system of Navier-Stokes equations with closure using a turbulence model and detailed chemical kinetics. To validate the results, Beach-Evans-Schexnayder and Burrows-Kurkov experimental data are used. The influence of various kinetic mechanisms, models of turbulence, and boundary conditions on the solution obtained is considered. The boundaries of the methods are shown.