A new and simple method is presented to determine the independent shard module of inversely isotropic materials. The method is treated on Green River Formation oil shale, one of such materials. The method is applicable for linear and non-linear elastic materials. Mathematical formulation, derivation and solution are given, and test apparatus and results are presented. Comparison with other approximate results and acoustical methods are made. Confirmation of the test method with materials having known shear module is also presented.