An analytical method is proposed for the response of the primary mass with an impact absorber having hysteresis damping. The impact absorbers in which motion of auxiliary mass is limited by motion limiting stop or placed inside a container. We tried to obtain the response curve of impact absorber subjected to periodic displacement excitation by the Fourier series method. Then, we analyze the response for the nonstationary random acceleration excitation by the simulation and equivalent linearization method. Some numerical results are shown.