Modeling of fractured reservoirs has always been one of the challenges of reservoir engineering science due to the structural complexities in describing the static model and the large number of equations in the dynamic model. Most of the natural fissured reservoirs have very little permeability in the rock mass and the fissures play the main role in guiding the fluid. The existence of a comprehensive numerical model of reservoir geomechanics with the aim of investigating the hydromechanical behavior of fractured reservoir rock is very important and necessary. Calculation accuracy along with high speed are two key factors in the success of any numerical method in producing an optimal model. In this research, it has been tried to use computational fluid dynamics technique to solve mass, momentum and structural equations for fluid and solid phases by considering capillary force equations. Also, efforts have been made to develop and test new numerical methods for numerical modeling of flow in highly heterogeneous and faulted reservoirs. The governing equations for immiscible two-phase fluid flow in a faulted compressible porous medium are derived. Another goal of this study is to discretize these equations using the standard finite element Galerkin method and using the interface element with zero thickness. One of the innovations of this study is the discretization of the governing equations in different states of fluid flow in the gap using the interface element. Also, in order to test the accuracy of the proposed method, several examples have been solved in fluid flow modeling. The results of the model presented in this study show a very good agreement with the existing results of the problems. All numerical equations and methods have been solved in the coding environment with Fortran and MATLAB software.