Abstract: Numerical simulations of explosion and impact problems have important engineering application value in the fields of national defense and civil security. Numerical simulations for these problems have a lot of di culties because the explosion and impact problems are strongly nonlinear transient dynamic problems in which multi-material mechanical behaviors are involved under the condition of high strain rate, high temperature and high pressure. Therefore, in this paper , the pseudo arc-length method for 3D nonlinear hyperbolic conservation system is proposed and the process of the algorithm realization is analyzed. The numerical results show that the algorithm improves the resolution of the shock wave strong discontinuity e ectively. The additive Runge-Kutta method for gaseous detonation numerical simulation is developed. In this method, the nonlinear convection part is solved implicitly while the chemical reaction source part is handled explicitly. The results show that the additive Runge-Kutta method can well capture and accurately describe the complex structure and typical characteristics. The parallel Eulerian numerical method of 3D multi-material hydrodynamics is investigated for the requirement of large-scale computation in engineering practical physical problems. The 3D explosion and impact problem parallel computation hydrocode is developed and the test method for this parallel hydrocode is proposed. According to the above works, some problems of large-scale and high-precision calculations for explosion and impact problems are solved. Finally, the experimental and numerical investigations on heavy-caliber shaped-charge penetration in thick concrete target are carried out, and the e ectiveness of the proposed numerical method is demonstrated by typical explosion and impact engineering problems.