Hydraulic Fracturing is a well stimulation technique which recently has been widely used for shale gas extraction. Hydraulic fracturing is when a fluid is injected into the wellbore under controlled pressure and flow. The differential pressure generated by the injection of fluid initiates cracks that will propagate into the deep-rock formations, so that it allows the extraction of hydrocarbons trapped into the rock. The technique is used in conventional and unconventional reservoirs of hydrocarbons. In the first case, in conventional reservoirs, the technique is applied in order to increase the production of the well, while in unconventional reservoirs (shale gas) the technique is used to enable the extraction of the gas due to its very low permeability. Furthermore, the process of fracturing the rock at great depths involves the control over the type of fracture created or reactivated, as this will depend on a number of factors. The study of the technique is important to improve the control over the execution of this procedure and also to avoid possible contingencies and accidents. A formulation was implemented in this work capable of representing discontinuities in a continuous mesh using a finite element code. The Extended Finite Element Method (XFEM) was implemented in a hydro-mechanical coupled formulation. Additionally, analyses were performed to identify how the permeability of the rock and the permeability of the fracture influence the hydraulic fracturing. As a result, it was observed that maintaining all of the mechanical properties constant, the hydraulic properties have a great impact on the hydraulic fracturing process. Also, the velocity of propagation of the fracture is affected by the permeability of the rock, and its ratio is inversely proportional
