An undamped two-degree-of-freedom vibro-impact system with a harmonic excitation is studied based on the theoretical analysis by Poincare map.A criterion for the existence of single impact period-1/n motions is obtained,and the initial position of the subharmonic periodic motion can be determined.The stability and the bifurcation of periodic motions are studied by computing the characteristic values of the Jacobian matrix.A combination of analytical and numerical techniques is proposed in the study of periodic motions of vibro-impact systems.