Abstract: A new fast computational method for one-dimentional unsteady gas flow with shock wave is developed. The differential equations and boundary conditions in new. Lagrangian variables are formulated. We calculated a specific case that the piston is moving with constant acceleration. In this example the position of the Shock wave is found with good accuracy. Before the formation of the shock wave, the simple wave has an exact solution. Comparism of our computational results with the exact solution shows satisfaction in accuracy.