In this chapter, we simulate the problem of shock-wave penetration of a deformable hemisphere into a granular medium consisting of spherical steel balls. Large displacements and deformations of the bodies are taken into account. The granular medium is considered as an elastoplastic medium with irreversible deformations. Two numerical techniques developed for solving three-dimensional problems based on the application of the refined Godunov scheme, Euler-Lagrangian multigrid algorithms, and the DEM method were selected. This chapter presents the results of numerical simulation of the process of normal high-speed interaction of a deformable hemispherical body with a granular medium. The medium under consideration consists of spherical steel balls. Coulomb friction between particles and contacting bodies is taken into account. The dynamic behavior of a discrete porous medium under conditions of its compression is described using a model of a continuous elastoplastic medium and a numerical technique based on the DEM method. The results of numerical studies using the Godunov method and the DEM method are compared with experimental data.