The possibility of stabilizing the detonative combustion of hydrogen-air mixtures coming into an axisymmetric Laval nozzle with a high supersonic velocity under conditions of atmosphere at altitudes up to 24 km is being studied. The appropriate parameters for the composition of the mixture and the nozzle channel are determined. Used mathematical model is based on the non-stationary two-dimensional equations of an axisymmetric flow of an inviscid multi-component gas with non-equilibrium chemical reactions. A detailed kinetic model is used to describe the detonative combustion of hydrogen-air mixtures. The heat capacity and enthalpy of the mixture are calculated from the reduced Gibbs energy of the gas components. Numerical simulation is performed on the basis of Godunov's finite difference scheme and its modification of a higher order of accuracy. Most of the calculations are performed on a supercomputer "Lomonosov" of Lomonosov Moscow State University using OpenMp technology of parallel calculations. (C) 2018 Hydrogen Energy Publications LLC. Published by Elsevier Ltd. All rights reserved.