In this paper, the thermodynamically and mathematically consistent modeling of anisotropic materials under shock loading is considered. The equation of state used represents the mathematical and physical generalizations of the classical Mie–Grüneisen equation of state for isotropic material and reduces to the Mie–Grüneisen equation of state in the limit of isotropy. Based on the full decomposition of the stress tensor into the generalized deviatoric part and the generalized spherical part of the stress tensor (Lukyanov, A. A., 2006, “Thermodynamically Consistent Anisotropic Plasticity Model,” Proceedings of IPC 2006, ASME, New York; 2008, “Constitutive Behaviour of Anisotropic Materials Under Shock Loading,” Int. J. Plast., 24, pp. 140–167), a nonassociated incompressible anisotropic plasticity model based on a generalized “pressure” sensitive yield function and depending on generalized deviatoric stress tensor is proposed for the anisotropic materials behavior modeling under shock loading. The significance of the proposed model includes also the distortion of the yield function shape in tension, compression, and in different principal directions of anisotropy (e.g., 0 deg and 90 deg), which can be used to describe the anisotropic strength differential effect. The proposed anisotropic elastoplastic model is validated against experimental research, which has been published by Spitzig and Richmond (“The Effect of Pressure on the Flow Stress of Metals,” Acta Metall., 32, pp. 457–463), Lademo (“An Evaluation of Yield Criteria and Flow Rules for Aluminium Alloys,” Int. J. Plast., 15(2), pp. 191–208), and Stoughton and Yoon (“A Pressure-Sensitive Yield Criterion Under a Non-Associated Flow Rule for Sheet Metal Forming,” Int. J. Plast., 20(4–5), pp. 705–731). The behavior of aluminum alloy AA7010 T6 under shock loading conditions is also considered. A comparison of numerical simulations with existing experimental data shows good agreement with the general pulse shape, Hugoniot elastic limits, and Hugoniot stress levels, and suggests that the constitutive equations perform satisfactorily. The results are presented and discussed, and future studies are outlined.