The paper is present 3D numerical simulation data on elastoplastic deformation in auxetic single crystals with account of anisotropic pressure. The use of anisotropic pressure allows us to demonstrate the absence of shock wave splitting into an elastic precursor and a plastic wave in a Zn single crystal in the loading direction [0001]. This effect in Zn single crystals is observed in full-scale experiments at any loading rate in the [0001] direction. It is shown that anisotropic pressure should be entered into mathematical models of materials whose elastic properties are characterised by five and more independent elastic constants and hence by bulk compression anisotropy. The use of isotropic pressure in simulating the deformation of such materials leads to nonphysical results.