In order to analyze the dynamic characteristics of the alternating hydraulic impact machine and the rebound of the impact piston, the mathematical model and the AMESim numerical model of the alternating hydraulic shock system are established. And the numerical model parameters are calculated and set according to the structural parameters and working parameters of the impact machinery. The numerical simulation results show that the oil supply parameters and the stiffness of the working medium have a great influence on the dynamic characteristics of the impact piston. The rebound of the impact piston will increase its impact frequency, reduce the single impact energy. The value and trend of AMESim numerical simulation and mathematical model are consistent, which fully prove the correctness of modeling. The model can provide theoretical basis and practical reference for the rapid design and performance analysis of such alternating hydraulic shock system.