Stress wave which is caused either by an explosion in a borehole or by an accidental explosion in a tunnel is supposed to be considered under certain circumstances when it propagates through the surrounding rock masses which contain holes in cylindrical form. Studying the ground motion induced by the cylindrical wave propagation is of practical significance for underground rock engineering and underground energy exploitation. The current study presents a numerical study on the ground motion caused by cylindrical P-wave propagation across a rock mass with a structural plane using a discrete element numerical method, UDEC. Firstly, the accuracy and validity of the cylindrical wave propagation simulation in UDEC and of the induced ground vibration are confirmed by comparison with the theoretical results for a special case that there is no structural plane in a rock mass. Secondly, cylindrical wave propagation across a rock mass with a structural plane is simulated, and then, the particle velocity on the ground surface is subsequently obtained. Finally, parametric researches are carried out on the influence of the monitoring point’s position, the structural plane stiffness, and the frequency of incident wave on the peak particle velocities (PPVs) of the ground vibrations.