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In this work, the orientation and propagation of cracks in fretting fatigue problems is analyzed numerically using the finite element method (FEM) and the extended finite element method (X- FEM). The analysis is performed by means of a 2D model of a complete-contact fretting problem, consisting of two square indenters pressed onto a specimen subjected to cyclic fatigue. For the simulation, we allow for crack face contact in the implementation during the corresponding parts of the fatigue cycle. The problem is highly nonlinear and non-proportional and we make use of the so-called minimum shear stress range orientation criterion, min(Delta tau), proposed by the authors in previous works. This criterion is introduced to predict the crack path in each step of the crack growth simulation. The objective of the work is to detect which is the relevant parameter affecting the crack path orientation. A parametric study of some a priori relevant magnitudes is carried out, such as normal load on the indenters, bulk load on the specimen, stress ratio and relative stiffness of the indenter and specimen materials. Contrary to previous expectations, it is shown that the relative magnitude of the applied loads has no significant effect. However, it is found that the stiffness of the indenter material with respect to the specimen material has the greatest effect. A simple explanation of this behavior is also provided.