The compressive strength as a function of confining pressure and sample orientation was determined for three anisotropic sedimentary rocks (slate and two types of shales). The samples were tested over a confining pressure range of 0 to 40,000 psi, with pore pressure held constant at atmospheric pressure. The orientation of the plane of anisotropy (bedding or cleavage plane) was varied between 0 and 90 deg relative to the axial load. The test results indicate that anisotropic sedimentary materials fail or deform by shear along the bedding plane, shear across the bedding plane, plastic flow along the bedding plane, or internal buckling depending upon the orientation and/or the initial stress state. The strength data gathered were compared to three basic failure theories for anisotropic materials: (a) Walsh-Brace modification of Griffith’s theory; (b) single plane of weakness theory; (c) variable coefficient of friction and cohesive strength theory. It was found that over certain pressure ranges and orientations all three theories fit the experimental data. On the basis of experimental data an empirical relationship was proposed to be used in conjunction with the variable coefficient of friction and cohesive strength theory. This modified theory produced a good fit of the experimental data over all orientations.