Abstract: Based on Muskhelishvili's complex potential theory and using the boundary conditions on crack faces and the single value condition of displacement in an infinite plane, the crack problem under compressive loadings is transformed into a Hilbert problem and the fundamental solutions for cracks with different surface patterns due to concentrated pseudo-tractions are derived. For different surface patterns, the value and the distribution condition of the shear stress are analyzed in detail, and a new computing model is developed. With the aid of the pseudo-traction method, the superposition technique and the presented fundamental solutions, a method to obtain the stress intensity factors (SIFs) for materials such as rock with central inclined cracks under compressive loading is proposed. The study indicates that the surface pattern has no effect on K_Ⅰ, but has obvious effect on K_Ⅱ. Under the same condition, both the breaking angle and the breaking mode of cracks are affected by different surface patterns.