Fatigue is the most common source behind failures of mechanical structures. In order to study the phenomena, experiments have been performed by Lloyd's Register and other tests have been presented in literature. Performing real life fatigue experiments requires a long time, a considerable amount of money and it is size limited. The solution is to create and validate numerical models which are accurate and reliable. This is the main reason why the research is focusing on the prediction of the crack growth, using numerical models. The reference geometry for this study is a plate with longitudinal stiffener, since a lack of knowledge about this shape has been noticed in literature. In order to better understand the current knowledge in the topic of fracture mechanics, an extensive literature review has been performed. Considering a plate with longitudinal or transverse stiffener, the crack always appears at the weld toe, and propagates with a charactheristic semi-elliptical shape. The empirical solutions needed to compute crack propagation are presented in the British Standard 7910 (BS7910), but additional correction factors have been described in literature Anderson, 2005, Bowness and Lee, 2000, Han et al, 2014 and Newman and Raju, 1981. An additional research has been performed about the 3D modeling using the finite element method. The standard FEM can be used to compute the Stress Intensity Factor (SIF) along with a dedicated "spider web" mesh around the crack front. A valid alternative is marked by the newly introduced XFEM method, which uses an element definition with additional terms; these terms are able to consider the crack discontinuity and the stress singularity at the crack tip. The empirical equations and the correction factors have been merged in 14 sets of equations. The objective of this first study is to assess the conservativeness of the solution proposed in the BS7910. A MATLAB empirical model has been created with the equations and the Paris law crack growth. The results of these models are compared to tests from literature and to the experiments from LR. An high accuracy is achieved using the set of equations from the BS7910 and using the correct load ratio. The FEM model has been created to define a new XFEM meshing technique able to supply accurate SIF results; finally, as demonstration of the accuracy of the XFEM models, the empirical equations has been compared with the 3D finite element models. An extensive mesh convergence study was performed, reaching a good agreement for the crack in a simple plate, both using the standard FEM method and the newly introduced XFEM solution. Finally, a comparison between the new XFEM mesh and the standard mesh in a plate with transverse stiffener was performed. This latest comparison highlighted a big discrepancy in the SIF solution for the surface point of the semi-elliptical crack. This difference was demonstrated to be the consequence of an erroneous stress distribution in the standard FEM model. The research has brought to the conclusion that the empirical model using the BS7910 is able to deliver accurate results, if the correct load ratio is considered. While in the FEM model analysis, it has been demonstrated that the empirical equation from Bowness and Lee, 2000 is not accurate at predicting the stress intensity factor at the surface point. This finding was revealed thanks to the use of the XFEM finite element method along with a detailed meshing technique.