Abstract: The study on rock strength based on fracture mechanics is still a significant project in the field of fracture mechanics and rock mechanics. Through the analysis of shear failure mechanism of a single linear crack under compression, the physical mechanism of compression-shear fracture toughness for tensile failure was investigated, and the corresponding solving method was also presented. A set of complex stress functions is proposed and by using the boundary collocation method (BCM), the dimensionless coefficients of stress intensity factors (SIFs) for a cracked specimen under compression was obtained. By using the SIF dimensionless coefficients, the compression-shear fracture criteria for tensile failure was improved and the formula of compressive strength of fractured rock specimens was derived. An example was presented to demonstrate the reliability of the method introduced in this paper. Finally, the effects of friction coefficients, crack orientation, crack length, cohesion, and confining pressure on rock compressive strength were discussed.