The objective of this paper is to consider the thermodynamically consistent anisotropic plasticity model based on full decomposition of stress tensor into generalized deviatoric part and generalized spherical part of stress tensor. Two fundamental tensors and , which represent anisotropic material properties, are defined and can be considered as generalizations of the Kronecker delta symbol, which plays the main role in the theory of isotropic materials. Using two fundamental tensors and , the concept of total generalized “pressure” and pressure corresponding to the volumetric deformation is redefined. It is shown that the formulation of anisotropic plasticity in the case of incompressible plastic flow must be considered independently from the generalized hydrostatic pressure. Accordingly, a modification to the anisotropic Hill criterion is introduced. Based on experimental research, which has been published, the modified Hill (1948, “A Theory of the Yielding and Plastic Flow of Anisotropic Metals,” Proc. R. Soc. London, Ser. A, 193(1033), pp. 281–297; 1950, Mathematical Theory of Plasticity, Clarendon, Oxford) criterion for anisotropic elastoplasticity is validated. The results are presented and discussed, and future studies are outlined.