This report presents a method of utilizing the coulomb strength criteria for estimating the strength and stability of pillars and pit slopes containing planes of weakness. It is assumed that the coulomb theory, as a special case of the mohr envelope, is a satisfactory first approximation of failure in uniaxial compression or triaxial loading with low lateral loads. Accepting this assumption for brittle materials, an expression for the strength decrease of rock pillars containing a plane of weakness or fracture at any angle of orientation is derived. As few as six samples (three solid cores and three fractured cores at a failure-oriented angle) are required for testing uniaxially and triaxially to statistically determine the coefficients of friction and the shear strengths of both the solid rock and the fracture plane and the range of failure angles of the fracture plane. Interpretation of the data shows that the mean normal stress and maximum shear stress technique of analyzing the data is superior for solid core and that shear and normal stress values using angles of failure should be used for fractured specimens with failure-oriented angles.