In order to model the mechanical behavior of joints efficiently, a thin-layer tri-node joint element is constructed. The stiffness matrix of the element is derived in the paper. For it shares the common nodes with the original tri-node triangle element, the tri-node joint element can be applied to model the crack propagation without remeshing or mesh adjustment. Another advantage is that the cracked body is meshed without consideration of its geometry integrity and existence of the joints or pre-existed crack in the procedure of mesh generation, and then the triangular element intersected by the crack or joint is automatically transformed into the tri-node joint element to represent pre-existed cracks. These make the numerical simulation of crack propagation highly convenient and efficient. After CZM is chosen to model the crack tip, the mixed- energy simple criterion is used to determine whether the element is intersected by the extended crack or not, the extended crack is located in the model. By modeling the marble plates with two edge cracks subjected to the uniaxial compressive loads, it is shown that the numerical results are in good agreement with the experimental results, which suggests that the present method is valid and feasible in modeling rock crack propagation.