The main objective of this work has been the validation of a methodology to calculate the Stress Intensity Factors (SIFs) in prospective cracks of offshore mooring chains under service conditions. For this purpose, the analytic methods described in the B57910 have been compared with those calculated by the conventional Finite Element Method (FEM) by means of contour integrals and by the Extended Finite Element Method (XFEM) implemented in the Abaqus 2018 software. First, an axially loaded cylinder has been studied in order to determine the correlation between different methods for a simple case, as well as to establish the most suited finite element methodology. Then, the real case of a mooring chain has been studied, including the residual stresses induced in the manufacturing process. Finally, numerical simulations and experimental results have been compared. Results justify the use of numerical methods, specifically the use of contour integrals, for the calculation of Stress Intensity Factors (SIFs) in offshore mooring chains.