The objective of this study is to describe the inequalities of anisotropic rock physics. Anisotropic rock physics provides the link between seismic anisotropy and anisotropic properties of rocks. However, the limitations of anisotropic rock physics predictions and measurements are not well understood. In this study we provided rock physics inequalities as guidelines to check the validities of anisotropic rock physics predictions and lab measurements. Initially we used Rudzki’s inequalities for TI media; then we provided proof of concept of these inequalities as well as extended these inequalities for isotropic media. In addition, we verified these inequalities using published moduli of isotropic crystals, and finally we used these inequalities to check the qualitiy of rock physics predictions and measurements. For spherical pore structure where isotropic self-consistent (SC) rock physics approximations are equal to the anisotropic SC rock physics approximations, inequalities satisfy the rock physics predictions for porosity up-to 60%. With increasing the complexity of pore structure where isotropic rock physics approximations are not equal to anisotropic rock physics approximations, rock physics inequalities describe that part of the anisotropic SC rock physics prediction are not valid for transversely isotropic media. We found these invalid predictions are associated with a higher anisotropic constant. Laboratory measured anisotropic velocity data which have a lower anisotropic constant (less than 0.6) satisfy theses inequalities. However, measured results for clay minerals (e.g. illite and kaolinite) which have a higher anisotropic constant (above 0.6) do not satisfy these inequalities. We concluded these unsatisfied anisotropic rock physics predictions and measurements should be treated as higher anisotropic media (orthorhombic, monoclinic) than transversely isotropic media.