This paper presents a boundary element method combined with the maximum tensile stress criterion for predicting crack initiation angles and simulating fracture propagation paths in cracked anisotropic plates under mixed mode loading. Since the calculated displacements near the crack tip by the BEM have been verified to be very accurate, a decoupling technique can be used to determine the mixed mode stress intensity factors based on the definition of the J‐integral and the relative displacements at the crack tip. Numerical examples are presented for the calculation of stress intensity factors for both isotropic and anisotropic cases. It can be found that our numerical results are in good agreement with those reported by previous authors. Fracture propagation in an anisotropic plate under mixed mode loading is simulated by an incremental crack extension with a piece‐wise linear discretization. A computer program, which can automatically generate a new mesh (required for analyzing sequentially the boundary configuration) has been developed to simulate the fracture propagation process. It was found that the numerical analysis could predict relatively well the direction of crack initiation and the path of fracture propagation.