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This paper analyzes the initiation and propagation of hydraulic fracturing by nonlinear numerical modeling. A notch located at the wellbore stimulates hydraulic fracturing. The notch has a pivotal role in hydraulic fracturing. There is evidence that the notch can affect the required fluid pressure and the fracture propagation and velocity. Therefore, it has been associated with the effectiveness of hydraulic fracturing in tight gas reservoirs. The objective of this study is to explore the effect of the notch angle on hydraulic fracturing. Models in two-and three dimensions are presented and analyzed. These models are used to find the breakdown pressure and stress intensity factors, respectively. The numerical approximation of hydraulically driven fracture propagation is based on the extended finite element method (XFEM). XFEM enriches finite elements and nodes at elements intersected by the crack during the crack propagation. XFEM reproduces the discontinuity in the displacement domain without the discretization of this property directly in the mesh. Therefore, the generated mesh is independent of the crack propagation. The accuracy of the numerical approach is validated by reproducing laboratory-scale hydraulic fracturing tests and comparing results.