The paper describes some aspects of the application of XFEM to represent Geomechanical discontinuities, including the choice of additional nodal variables and the appearance and remedies to the oscillations that may take place depending on the mesh layout. An example of application to recover the stresses along a discontinuity line emanating from a tunnel cross-section is presented together with the comparison to an analytical solution. The formulation is developed in terms of the “overhang” displacement variables on the other side of the discontinuity (instead of more traditional displacement jump variables), and the oscillations associated to nodes too close to the discontinuity are solved by moving those nodes onto the discontinuity (instead of moving them away as seems more common in current practice).