Abstract: A numerical solution of the shock-turbulent boundary layer interaction over a compression corner for supersonic flow is presented.The computation consists of the Cebeci-Keller Box scheme for obtaining non-similar solutions of the boundary layer equations and the unified supersonic-hypersonic small disturbance theory over a wedge for obtaining the inviscid pressure distribution.The initial inviscid pressure distribution is calculated by the oblique shock relations.Due to the existence of the boundary layer, the pressure rise across the oblique shock may be flattened throughout a distance equal to several thicknesses of the boundary layer in the vicinity of the corner.The boundary layer computation begins at §=0 with εm=0, which corresponds to laminar flow. Then the turbulent boundary layer is calculated at the following stations.The viscous-inviscid coupling is through factor P2 which is related to the local surface inclination through Eqs（33）, The inviscid solution provides a new value of P2 for boundary layer computation. And the updated viscous parameters then provide a new displacement surface and its inclination for the inviscid calculation of the next iteration.The computation predicts the wall pressure distribution and the initial pressure rise location well.