In this paper, it is studied theoretically that a harmonic exciting displacements generate the stationary impact vibrations in such a mechanical system with two degrees of freedom as consists of two masses with a clearance. The conditions for maintaining stable periodic vibration are analyzed and ranges of parameters are determined where asymptotic stability is assured. It is found from the results of theoretical analysis and numerical calculation, that stable fundamental impact vibration occurs in a wide range of the exciting frequencies when the clearance between two masses is close to the exciting displacement and a sub-impact vibration occurs when the frequency is high, while a two-impacts vibration occurs as the frequency becomes low.