Application of Impact damper for reduction of vibration amplitude through momentum transfer is now well established. However, no literature is available for the effect of an impact damper on axial vibration of a rod as a continuous system. The equation for axial vibratory displacement of the rod, fixed at one end and a lumped mass at the other end, is derived by considering steady state vibrations having a period equal to that of the forcing function at the free end. Structural damping is assumed to be modal with a damping ratio of 0.005. Taking this periodicity into account, the repetitive impact force is resolved in the sinusoidal functions through Fourier series analysis. The forcing function thus will have components with the frequency of the external force and the multiple harmonic forces resulting from impacts. Since an infinite series is involved, the solution is obtained for a truncated series using MATLAB. It is observed that the damper is most effective when the Impact distribution parameter is equal to 0.5. The results of the numerical analysis are supported by experiments and are found to be in good agreement with the theoretical results. The reduction of vibration amplitude is observed to be dependent on the clearance (travel of impacting mass), mass ratio of the impacting mass to the main system, frequency of excitation, and the location of the stop in addition to the impact distribution.