Mixed mode fracture in rock subjected to compressive loading has many differ-ent features in fracture hehaviour from those subjected to tensile loading,especially when the aper-ture is partly or fully closed.The traditional theory of elastic fracttire mechanics can not be used tosolove compressive-shear fracture problem. Based on fracture characteristics of rock under compres-sion,the formulas to calculate stress intensity factor are updated so that the new strength criterion isevolved to evaluate the crack initiation streilgth.The stress distribution and the relative displacementof crack surface in central slit is confirmed by FEM analysis.