This paper introduces an application of the eXtended Finite Element Method (X-FEM) to the case of machining simulation, which is still subjected to numerical limitations. The treatment of the contact problem at the tool/chip interface is presented, and highlights the interest of the coupling of X-FEM with the Level Set method. Validation results are detailed through typical examples. We then present the first simulations of chip formation, using a Newtonian fluid law for the machined material, and extract the future improvements that the method is able to provide to cutting numerical simulation.