Abstract: In order to explore the fracture mechanism of open cracks under compression-shear stress in rock-like materials, a relative passivation coefficient and a relative critical size are introduced, and a compression-shear-tension fracture criterion considering the geometric characteristics of cracks and T-stress is established. The effects of different factors on the distribution of tangential stresses and initiation angle of cracks are investigated. The predicted curves of the initiation angle of cracks are improved obviously because of considering the relative passivation coefficient, and the different fracture behaviors induced by crack length and material properties can also be explained after considering the T-stresses. In order to validate the theoretical solutions, the calculated results are compared with the test ones of several typical rock-like materials. It is found that when the relative passivation coefficient is small, the predicted values obtained by the proposed method agree well with those obtained from the tests, and the range of predicted angle is large. With the increase of the relative passivation coefficient, the error between the theoretical values and the test results increases gradually, and the range of predicted angle decreases slowly. The reason for this phenomenon is explained, the flaw of the fracture criterion based on the linear elastic fracture mechanics is discussed, and the applicable conditions of the proposed criterion is suggested.