The object of this study was to investigate the effect of anistropy on wedge indentation tests. These tests are used to qualitatively investigate the deviation forces encountered when drilling through an anisotropic medium. The preliminary investigation of anisotropic rocks lead to the study of an elastic - linear hardening limestone, Cordova Cream Limestone, also known as Austin Chalk. A yield condition and hardening rule, which could accurately account for the strain induced anisotropy, were developed. After carefully weighing the advantages and disadvantages of using this rock in wedge indentation tests, it was decided not to proceed further with this material. Instead, Pierre Shale was used, because preliminary tests indicated a high degree of anisotropy. Conventional triaxial tests were performed, in order to establish a yield condition. This yield condition was used in conjunction with four different theories to predict the vertical and horizontal forces encountered in wedge indentation tests. The four theories consisted of an adaptation of R. McLamore's preferred chip analysis, a plane strain slip-line field solution assuming no lip and a perfectly rough wedge, and two limit analysis solutions using the plane strain yield condition; one assumed a perfectly rough wedge while the other assumed the wedge to be frictionless. The slip-line field solution and the limit analysis solutions successfully bounded the vertical force data. The slip-line and limit analysis solutions for the horizontal force very nearly coincided. Although the scatter in the horizontal force data prevented quantitative confirmation of any of the above theories, the general trends, direction of forces and symmetry, were supported. The scatter in the data also did not convincingly confirm or contradict McLamore's theory, although previous observations and experiments do contradict this theory while supporting the plasticity solutions. Additional tests with various wedge and rock orientations were also performed to investigate the effects on the problem. The conclusions that can be made from this study are: (1) That the strength characteristics of Cordova Cream Limestone can be modeled successfully with Ziegler's modification of Prager's hardening rule in the principal stress space. (2) That plasticity theory can successfully predict the forces on a wedge penetrating anisotropic Pierre Shale. The consequences of this study are that the forces on the wedges and therefore on a drill bit are in the up-dip direction when the bedding plane is inclined less than 45°, while the forces are in the down-dip direction for inclinations greater than 45°.