Abstract: A streamline upwind/Petrov-Galerkin (SUPG) weighted residual formulation has been developed in the present paper for the quasi-simplified N-S equations. Numerical calculations have been made for the Burgers' equation, the shock reflection on a solid wall, and the supersonic laminar flow over a flat plate and two-dimensional compression corner flow by using the present method. The numerical results show that the present method has good accuracy, convergence, and stability properties.