Abstract: In this paper, the equations of motion governing the axisymmetric elastic deformation of finite circular cylindrical shells, including the effect of transverse shear and rotational inertia, are considered. By applying Generalized Ray Method, the ray formulus of the displacements and the internal resultant forces of the shell in the phase space are derived, then the solutions of transient elastic waves in the finite cylindrical shell subjected to the axisymmetric impact are obtained numerically by using FFT.