In this paper we present a numerical model for hydraulic fracturing purposes. The rock formation is modelled as a poroelastic material based on Biot’s Theory. A fracture is represented in a discrete manner using the eXtended Finite Element Method (X-FEM). The fluid flow is governed by a local mass balance. This means that there is an equilibrium between the opening of the fracture, the tangential fluid flow, and the fluid leakage. The mass balance in the fracture is solved with a separate equation by including an additional degree of freedom for the pressure in the fracture. The fracture can grow in arbitrary directions by using an average stress criterion. We show a result of hydraulic fracture propagation for a 2D circular borehole. The fracture direction is consistent with the expected direction.