In this thesis, the basis for a general implementation of the Thick Level Set method is presented. This basis combines the general applicability of the TLS_V1 method by Moës et al. with the improved fracture mechanics of the TLS_V2 method by Lé et al. In order to accomplish this, the topological skeleton needs to be found for an arbitrary configuration of the iso-0 curve, and mapped onto the mesh. Additionally, a discontinuity in the displacement field needs to be applied on the skeleton curve. Since the iso-0 curve that determines the skeleton curve can be arbitrary, the displacement jump also needs to be designed for an arbitrary skeleton curve. For the deterimination of the location of the skeleton curve, this thesis relies on a combination of the shrinking ball method by Ma et al. and Prim’s algorithm. The resulting skeleton curve is then mapped onto the mesh using a newly developed set of algorithms. Having mapped the skeleton curve onto the mesh, the displacement jump is then modeled using the phantom node method by Hansbo and Hansbo. During verification of the model, it is shown that the skeleton curve could be found for virtually any acyclical iso-0 curve. If the iso-0 curve was not acyclical, a single segment would be missing from the skeleton curve. Furthermore, it is demonstrated that the phantom node method can be used to define the displacement jump on the skeleton curve. Lastly, a mesh refinement study has been performed, which compared the results of the proposed model for 5 different mesh sizes. It was found that, for the rail shear test that was used to perform the verification, the shape of the iso-0 curve can vary randomly when the mesh is refined. The load-displacement curves, however, do not show significant dependence on the mesh size.