The Finite Element Method (FEM) has been and is one of the most used numerical methods for the estimation of characterizing parameters in Fracture Mechanics. In the case of Linear-Elastic Fracture Mechanics (LEFM), a number of procedures exist which allow the evaluation of the stress intensity factor K (or equivalently, the energy release rate G) from a finite element analysis (FE). This analysis has enabled to study crack propagation and life estimation issues. In recent years the application of Extend Finite Element Method (X-FEM) has proved a very effective tool for numerical modelling of cracks in MFEL, which provides significant benefits in the numerical modelling of crack propagation. The main advantages are that the finite element mesh need not comply with crack boundaries to account for the lack of geometric continuity, and also, mesh regeneration is not necessary in the crack growth simulations. Therefore, a single mesh, which is often generated easily, can be used for any crack length and orientation. The contributions made in this Thesis are related to three aspects: modelling of crack face contact with X-FEM, modelling of the propagation direction in fretting fatigue with complete contact and life estimation, also in complete contact. In the last two cases, the numerical estimations have been correlated with experimental results. Some fatigue problems may exhibit situations of contact between crack faces along the cycles, and therefore, cracks experience contact closure processes between their faces. This Thesis will utilize a mortar-based formulation to set the contact between the crack faces. A segmentation of the crack is performed based on the intersection with the underlying mesh. Also, the method X-FEM has been implemented in the program ABAQUS, which has allowed to implement the crack face contact routines in X-FEM through point constraints and by the mortar method. Moreover, crack initiation in fretting fatigue in complete contact conditions (using multiaxial fatigue criteria) has been studied. We have simulated the crack propagation path in its two phases I/II using X-FEM, through the application of traditional orientation criteria and other criteria proposed in this Thesis. Finally, the effect of the values of KI obtained by X-FEM has been studied. It has been compared with the values obtained analytically for the life estimation in fretting fatigue in conditions of complete contact, also studying the effect of multiaxial fatigue criteria and the effect of propagation laws in the life estimation.