Abstract: Based on the peridynamic theory, the strain energy density (SED) criterion is introduced to reflect the failure characteristics of rock-like materials. At the same time, the critical failure condition obeying the Weibull distribution is used to describe the heterogeneity of rock, which makes up for the deficiency that the peridynamic method cannot reflect the strain-softening characteristics and heterogeneity of rock when simulating the crack propagation of rock materials. The peridynamic method based on the SED criterion is used to simulate the crack propagation process of rock with single crack with different dip angles under uniaxial compression. The propagation mechanisms of airfoil cracks, secondary coplanar shear cracks and anti-airfoil cracks are analyzed. The proposed method is used to simulate the crack propagation process of rock with double parallel cracks under uniaxial compression. The results show that the failure process of rock with double parallel cracks can be divided into three stages: the first penetration of airfoil cracks, the second penetration of shear cracks to form a closed failure ring, and the formation of macro-cracks leading to failure. Finally, the simulated results are compared with those of the previous laboratory tests and numerical simulations to verify the effectiveness of this method. Through comparison, it is found that the proposed theory can better simulate the process of crack propagation of rock materials and has a good application prospect.