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Fluid injection and production cause changes in reservoir pressure, which result in deformations in the subsurface. This phenomenon is particularly important in reservoirs with abundant fractures and faults because the induced slip and opening of the fractures may significantly alter their hydraulic properties. Modeling strongly coupled poro-mechanical processes in naturally fractured reservoirs is a challenging problem. The Discrete Fracture Model (DFM) is a state-of-art method for modeling coupled flow and mechanics in fractured reservoirs. This method requires constructing computational grids that comform to fractures, which is very challenging in complex 3D settings. The objective of this study is to develop a numerical method that does not require gridding near fractures and can efficiently model hydromechanical interactions in fractured reservoirs. We utilize formulations based on the Strong Discontinuity Approach (SDA) for mechanics and Embedded Discrete Fracture Model (EDFM) for flow. We first present a mathematical formulation and emphasize the kinematic aspects of fracture slip and opening. We then introduce a series of mechanical tests that investigate the spatial convergence of the model and compare its accuracy with the Discrete Fracture Model (DFM). We finally consider a synthetic coupled case of a reservoir with several fractures and compare the performance of the SDA and DFM methods. Our results indicate super-linear spatial convergence of the proposed SDA algorithm. Numerical simulations confirm the applicability of the proposed method to modeling the coupling effects in subsurface applications.