The extended Wittrick-Williams algorithm combined with the precise integration method is used to compute the propagation of non-stationary random waves in anisotropic materials.The responses of the surface due to the non-stationary random excitations of the bedrock are investigated.Based on the natural frequencies and modes computed by means of the pseudo excitation method and the precise integration method in combination with the extended W-W algorithm,the mode-superposition scheme are jointly used to solve the differential equation of non-stationary random wave propagation in layered anisotropic materials.The power spectral density of the surface random responses is thus obtained.