The paper presents the results of mathematical modeling of mixing and ignition of hydrogen jets in supersonic flow. Calculations were carried out on the basis of the Favre-averaged Navier-Stokes equations supplemented with k - ω SST turbulence model and detailed chemical kinetics. The solution was carried out in three stages. At the first stage, the kinetic schemes were tested by comparison with the experimental data on ignition of the hydrogen round jet supplied co axially with the M=2 air jet into the still air. The second 2D task was to study the process of mixing and ignition of hydrogen jets fed at various angles into the M=3 air flow at the channel with a cavity. At the third stage, the 3D problem of hydrogen jets supplied normally to a primary M=4 flow in the channel with backward-facing steps was computed under the condition of the experiments made at the hot-shot facility.