To explore and develop a simple and efficient method for simulating joint propagation, we take the element partition method (EPM) as a basic method and use the Mohr-Coulomb criterion in element partition. Since EPM takes advantage of geometric features of triangular elements to construct a special threenode contact element, it can simulate fracture propagation in the original mesh scheme. The Mohr-Coulomb criterion is a widely used failure criterion in geomechanics, which can accurately predict the failure behavior of geomaterials. Combination of EPM and Mohr-Coulomb criterion has advantages in simulating joint propagation. To validate the proposed method, failure processes of crack material with double crack subject to different confining stresses are simulated. The results show general agreement with experiments. Comparison between the simulated and experimental results suggests that the method can represent typical features of joint propagation and coalescence subject to confining stress.