Abstract: For numerical simulation of transition process from continua to discontinua, theⅠ/Ⅱ tensile-shear mixed mode fracture of quasi-brittle materials such as concrete and rock is analyzed by coupling respectively the smeared rotating crack model and the discrete crack model with deformable discrete element method(DEM). The zoning of tensile-shear failure criterion and the gradual reduction of stiffness and strength driven by the normal opening of crack are proposed based on the joint-contact constitutive relationship of deformable discrete element method. The models are applied to analyze the nonsymmetric three-point bending beam with a single-edge notch. The comparison between experimental and numerical results shows that the two nonlinear fracture models are both capable of predicting the initiation and propagation of the crack. It also shows that the crack initiateds withⅠ/Ⅱ tensile-shear mixed mode but steadily propagated predominantly in mode Ⅰ under mixed loading. It is also concluded that the discrete crack model based on DEM is capable of simulating the entire fracture to collapse process of the loaded system.