This paper studies elastic and elastoplastic deformation in anisotropic materials through numerical simulation of strain processes in anisotropic materials based on the zinc single crystal. The mathematical model implemented in this study reflects the following characteristics of the mechanical properties inherent in single crystals of zinc: anisotropy of elastic and plastic properties, auxeticity and anisotropy of volumetric compressibility. The results of strain processes in the spherical bodies composed of zinc single crystals exposed to dynamic loading by uniform compression pulse were obtained through numerical simulation in a 3D formulation. It was shown that the spherical body of a single crystal of zinc transforms into a two-axial ellipsoid with alternating change of the maximum elongation in mutually perpendicular directions during the propagation of elastic waves. When the propagation of elastoplastic waves in the initially spherical body that consists of single-crystal zinc occurs under its dyn...