Hydraulic fracturing is a significant technique in petroleum engineering to enhance the production of shale gas or shale oil reservoir. The process of hydraulic fracturing is extremely complicated, referring to the deformation of solid formation, fluid flowing in the crack channel, and coupling the solid with fluid. Simulation of hydraulic fracturing and understanding the course of the mechanism is still a challenging task. In this study, two hydraulic fracturing models, including the Khristianovic−Geertsma−de Klerk (KGD) problem and the hydraulic fracture (HF) intersection with the natural fracture (NF), based on the zero thickness pore pressure cohesive zone (PPCZ) element with contact friction is established. The element can be embedded into the edges of other elements to simulate the fracture initiation and propagation. However, the mesh type of the elements near the PPCZ element has influences on the accuracy and propagation profile. Three common types of mesh, triangle mesh, quadrangle mesh, and deformed quadrangle mesh, are all investigated in this paper. In addition, the infinite boundary condition (IBC) is also discussed in these models. Simulation indicates that the results of pore pressure for zero toughness regime simulated by the triangle mesh are much lower than any others at the early injection time. Secondly, the problem of hydraulic fracturing should be better used with the infinite boundary element (IBE). Moreover, suggestions for crack intersection on the proper mesh type are also given. The conclusions included in this article can be beneficial to research further naturally fractured reservoirs.