The fracture process of quasi-brittle materials requires special attention for the prediction of the direction of fracture propagation. The fracture simulation with the finite element method (FEM) has as its disadvantage the dependence of the fracture trajectory with respect to the mesh adopted. Besides, there is some difficulty for numerical models to represent the fracture in mixed mode because of the parameters involved. The Extended Finite Element Method (XFEM) is a technique which combines the FEM with enrichment functions to represent discontinuities in the displacement field. In this context, this dissertation discusses the criteria for nucleation and propagation of fractures and their implementation in the context of XFEM. The implementations were made in the GeMA framework, a software developed at Tecgraf / PUC-Rio. The implemented crack growth criteria is based on the stress approach and allows to control different geometries and sizes of the evaluation area in the crack tip. A parametric study is presented for modeling a concrete beam under nonproportional loading with mixed-mode fracture. Different situations were taken into account such as mesh refinement, geometry and size of the evaluation region, crack initiation and propagation and solution control techniques. Also, several models with different loading and boundary conditions were made to validate the criteria under complex situations. The parametric findings obtained through the study of the beam proved to be valid for the other models. The implementations of the fracture propagation criteria in the XFEM demonstrated excellent agreement in the simulations of the fracture trajectories compared to the experimental data.