The overall aim of this paper is the development of nonlinear formulations of BEM (Boundary Element method) for the analysis of fracture problems and also the realization of a probabilistic approach to the fatigue problem through the coupling between a mechanical model that deals with the propagation of cracks under fatigue, and structural reliability models. On the BEM/MEF coupling model, the crack propagation model was introduced on a linear elastic regime. This model leads to interesting results and allows to analyse some structures where this effect is important. Closing the topic related to the development of BEM formulations, a formulation was also developed for the analysis of fatigue cracking propagation problems. Probabilistic models are applied to the analysis of structures submitted to fatigue. It is known that the integrity of the structures in service essentially depends on its ability to maintain a resistance pattern over time. To this probabilistic model was coupled an optimization algorithm for the determination of parameters such as the geometry dimensions of the structure as well as intervals for the performance of the maintenance and inspection procedures, taking into account objective functions written in terms of structural cost and safety. The investigation shows that direct coupling scheme converged for all problems studied, irrespective of the problem nonlinearity.