The improvement of the mixing of the injected jet fuel in the cross‐flow oxidant (jet in cross‐flow (JICF)) in the scramjet combustor is still remains opened problem. JICF is accompanied with the formation of shock structures and leads to the shock wave boundary layer interactions (SWBLI) at the walls of the combustion chamber. The purpose of this paper is to study the influence of the interaction of the bow shock wave with the upper boundary layer and shock wave (reflected from the upper wall) with lower surface flow behind the jet on the mixture layer mechanism. For that, the numerical simulation of a supersonic flow with a transverse multispecies jet injection from the bottom wall of the plane channel with variations of the channel heights and the jet pressure ratio is done. The multispecies supersonic gas flow in a planar channel with perpendicular jet injection is numerically simulated. The Favre‐averaged Navier‐Stokes equations coupled with the k‐ω turbulence model are solved using the fourth order weighted essentially non‐oscillatory (WENO)‐scheme. The simulation correctly captured the main flow features near the jet and the comparison with the experimental data shows a satisfactory agreement. The reflected shock wave, formed as a result of the interaction of a bow shock wave with the boundary layer (SWBLI), reaches the lower boundary layer behind the jet and interacts with them. The numerical experiments reveal show that this shock/wave interaction causes an oscillation of the flow. The channel height variations show that with a decrease of the height the mixing rate increased.