Abstract: An integral method associated with direct and inverse mode is presented for the calculation of compressible turbulent boundary layer with separations over airfoil. The method employs the momentum integral equation and a mean-flow kinetic energy equation, and makes use of Swafford' s velocity profile expression. Four different algebraic eddy viscosity models are used to evaluate the dissipation integral at each streamwise location. The effect on the boundary layer development is analysed. Comparisons are made with experimental data on the interaction between shocks and turbulent boundary layers over the transonic airfoil. Finally, the method is extended to handling airfoil wakes.