Abstract: In the studies on the initiation mechanism of cracks of rock in compression and shear, the traditional fracture theory only considers the singular stress (r^1/2 term) of the elastic stress state near a crack tip in the Williams’ series expression, and ignores the effects of the non-singular term (T-stress). It leads to the disagreement between the theoretical predictions and the experimental results. On the basis of analyzing the mechanical behaviors of cracks in compression and shear, the T-stress is introduced into the maximum tangential stress (MTS) criterion of the traditional fracture mechanics, and accordingly the revised MTS criterion is proposed by considering T-stress. Meanwhile, by considering the stress transfer of the cracks in compression and shear, the deformation parameters of cracks, e.g., the crack normal and shear stiffness, are also introduced into the original MTS criterion. Finally, the new MTS criterion is set up to simultaneously consider the properties of rock, the geometrical parameters of cracks (such as dip angle and length), the strength parameters (such as frictional coefficient of crack face), and the deformation parameters (such as crack normal and shear stiffness). Therefore, it can perfectly reflect the initiation mechanism of the cracks of rock in compression and shear. The example indicates that the initiation angle of wing crack obtained from the proposed method agrees well with that obtained from the tests, and it is also found through the sensitivity analysis for the parameters that the relative critical size at the crack tip has the most important influences on the initiation angle of wing crack.