Combustion process in a scramjet has been stimulated by a quasi-one-dimensional model. Quasi-one-dimensional code has been validated by comparison with HyShot-2, Billing, Anderson and Queensland University experiments. The specific impulse for a typical hypersonic aircraft have been calculated.Development of two-dimensional model, has been focused on the SCHOLAR experiment. Convective and radiative heating the inner surface of the chamber scramjet have been studied by numerical simulation. The unsteady viscous-inviscid interacting flowfield and combustion of a hydrogen-air mixture in supersonic flow paths are modeled through thermo-physic gasdynamic code. Fields of chemical species concentrations, pressure, and temperature are calculated by twodimensional (axisymmetric and plane) computational model based on the unsteady governing equations including Navier-Stokes equations, energy conservation and diffusion equations together with system of chemical kinetic equations.