Viscous-inviscid interaction is used to compute steady two-dimensional, transonic flows for the S-shape inlet. The inviscid flow solutions are obtained by solving the full potential equation in conservative form. The difference equations are solved using AF2 approximate factorization scheme. A finite-difference method is used for the boundary-layer solution. The coupling was performed by applying a surface transpiration velocity determined from the calculated boundary-layer growth. Results are obtained for laminar, transitional, and turbulent flows. An inverse boundary-layer finite difference procedure is also described for viscous flows containing separation bubbles. Results are compared with results obtained using boundary-layer integral method.