Abstract: Numerical solutions of supersonic separated flow over the compression corner with blowing and suction in the shock region are presented. The effects of blowing only or suction only on the shock boundary layer interaction are firstly studied. Then the emphasis is put on the flow with a combination of suction downstream and blowing upstream the shock, which is equivalent to the method of passive control of the shock boundary layer interaction. The results show that this control method has the potential to weaken the shock wave and reduce the shock induced separation tendency in the condition of supersonic flows. The numerical algorithm used in this paper is based on the pressure splitting form of the reduced Navier Stokes equations, and a multiple marching technique is applied to solve the discretised form of the RNS equations.