The need has become evident for a more thorough understanding of the causes of hole deviation when drilling through stratified formations. The approach to this problem herein is to analyze the forces between the bit teeth and rock and how they might affect horizontal deflection of the drill bit. This study is specifically concerned with methods of modeling the rock and bit tooth interaction so that valid predictions can be made of the actual behavior. The rock and bit tooth interaction is modeled by a vertical wedge indentation into the flat, level surface of an arbitrarily oriented transversely isotropic rigid - perfectly plastic medium. The transversely isotropic wedge is itself modeled by vertical wedge indentation into the flat, inclined surface of an isotropic medium with arbitrary orientation of the direction of maximum slope. An upper bound approximation method for predicting horizontal and vertical loads is developed using fundamental principles of plasticity theory and an experimental study conducted as verification of the method. It is demonstrated herein that the experimental behavior has been satisfactorily predicted by the theoretical analysis and that a limit analysis solution to the isotropic wedge indentation problem has been obtained. An approach to the analysis of the transversely isotropic problem is outlined as a possible introduction to further work on this problem.