Modeling of discontinuities (fractures and fault surfaces) is of major importance to assess the geomechanical behavior of oil and gas reservoirs, especially for tight and unconventional reservoirs. Numerical analysis of discrete discontinuities traditionally has been studied using interface element concepts, however more recently there are attempts to use extended finite element method (XFEM). The development of an XFEM tool for geo-mechanical fractures/faults modeling has significant industrial potential; particularly within the hydrocarbon industry where it could lead to improved predictions for porosity/permeability changes in coupled geomechanical reservoirs. In this paper, we present a novel methodology based on the extended finite element method (XFEM) to analyze the behavior of pre-existing multiple strong discontinuities (faults and/or fractures) in reservoir rock. Detailed mathematical framework leveraging XFEM for multiple discontinuities in rock masses has been derived. This XFEM based framework is robust enough to represent strong discontinuities independently of the mesh. The approximation of discontinuities is constructed in terms of Heaviside/junction functions which lead to additional unknowns to capture the displacement jump across and at intersections of joints. Our framework and algorithm are general in nature and can handle complex geo-mechanical problems with different loading conditions. For validation of the implemented mathematical framework using XFEM, we analyze the behavior of a rock sample with multiple discontinuities and compare displacement and stress with known theoretical solution. Triaxial3D loading examples involving multiple discontinuities are also presented to demonstrate the accuracy and robustness of the proposed methodology.