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The modeling of structures cracked by the finite elements is limited in terms of crack propagation. The work proposed within the framework of this thesis consists of a development presentation followed by a numerical implementation of the X-FEM method in view of a dimensioning by the fracture mechanics of cracked structures of several examples from the simplest to the most elaborated, begin with simple examples and at the end an application of the implementation of the XFEM method on a real model to analyze the crack propagation in order to show the efficiency of the XFEM method.