Abstract: A one-step difference scheme for solving two-dimensional steady state Navier-Stokes equations is proposed to solve supersonic and hypersonic viscous interaction problems near the leading edge of a flat plate.The scheme is considered and analysed with a model equation.It has second order accuracy in space for steady state problems and its stability condition is improved.The scheme is much simpler in comparison with the commonly-used two-step predictor-corrector difference scheme for N-S equations and also convenient for programing.Two viscous interaction problems are solved with the proposed scheme.One of them is with parameters M∞=20,TwT0=0.06,Re∞L=4×108;the other is with M∞=3,Tw=T0,Re∞L=103.The solutions are valid throughout the boundary layer,shock-wave structure and inviscid core.The results were compared with experimental data in good agreement.Numerical solutions show that the non-slip conditions can be used for weak viscous interaction.The computed results are helpful to understanding the physical nature of interaction problems.