The problem of theoretical prediction of the elastic stiffness parameter is important, as well as proper establishment of its theoretical bounds, which is extremely useful in the reliable estimation. We revise a formula for the lower bound , empirically derived by F. Yan with coauthors, based on their empirical inequality between two Poisson’s ratios in a transversely isotropic elastic medium; i.e., . In doing this, we consider a theoretical counterexample derived on theoretical grounds by J. Sarout leading to the opposite inequality . Our analysis on shale anisotropy (using published data on various shale samples) proves both inequalities to be true. Therefore, we can divide shale data into two groups: 1 and 2; i.e., group 1 we define by the inequality , and group 2 by . In the framework of the linear slip (LS) model, we found another restriction on two Poisson’s ratios , which must be satisfied in the LS model. In addition, we found that the theoretical formula for the in the LS model and the bound should be equal: . Also, we found that depends on the normal fracture compliance . We postulate that there is a critical compliance predicted by the LS model that marks the transition between two inequalities of Poisson’s ratios: , and . These inequalities become a part of a broader interpretation, in which the compliance acts as a transitional intermediate response (i.e., ) between the two shale groups 1 and 2. Each shale group (i.e., , and ) is assigned to different (i.e., and ), which imply differentiation of rock properties in two groups, such as different fluid saturation, as an example.