Based on continuum mechanics and rock dynamics,analyzed the micro-struc- ture damage of rock and the impulsive effect under high pressure water jet and developed the dynamic model.Further,on the assumption of that rock was homogeneous and iso- tropic,a computational model was established based on nonlinear finite element and Arbi- trary Lagrangian-Eulerian(ALE) method.The dynamic effect impacted on rock under high pressure water jet was simulated by the dynamic contact method.The propagation of stress wave in rock was numerically simulated at different impacting velocity.The results show that the propagation velocity of stress wave is proportional to the impacting velocity of high pressure water jet.The faster the impacting velocity is,the quicker the comedown of stress wave.