Time-Marching methods solving Euler equations are used for calculation of two-dimensional, steady, inviscid flow through a stationary compressor cascade. Calculation method is based on the Denton`s opposed difference scheme. A smoothing in the axial direction is used to increase the stability of solution. The computational grid consists of quadrilateral elements, one of which has four nodes at each corner and the grid points on the upper periodic boundaries are located one pitch away from those on the lower boundaries to satisfy the periodicity condition. Results of calculation show good agreement with other computational and experimental results, proving that the present method of calculation should be applied with confidence for the cascade flow with shock wave.