The out-of-plane bending of offshore mooring chains leads to a rapid deterioration of the chain, ultimately leading to failure in a period that is a fraction of the design-life. The deformation of the contact surface of the chainlinks leads to the interlocking of the link. This in turn causes the chain to behave like a bending beam. The combination of the chains behaving in this manner and the vessel movement leads to a bending moment in the chain link, especially in the top section, where the tensions are high. Due to the alternating nature of the loading, multiaxial fatigue effects cause chain failure. In this thesis, a literature study is performed, forming an introduction to the general concept of fatigue and the exploration of available methods. For multiaxial loadings, so-called critical plane methods are widely accepted as the most effective approach. This critical plane method search for the material plane experiencing most damage, according to the damage criterion that is assessed. Furthermore, a number of methods for the cycle decomposition are present. For uniaxial methods, the rainflow method is most used. Applying this method to multiaxial fatigue problems can lead to problems, which leads to the formation of alternative approaches. The other approaches being discussed are the Wang & Brown method and the Modified Wang & Brown method. The Bannantine & Socie method is discussed too, but could be classified as a critical plane search algorithm, instead of a novel cycle counting method. After the exploration of the problem, a finite element model is created. This model consists of multiple chain links, that are proofloaded while plastic deformation is allowed. This leads to the aforementioned deformation of the contact surfaces on the links. After the proofloading step is completed, three different cases are performed with an elastic material formulation. These cases comprise of varying angle ranges; Case 1 only induces an out-of-plane bending in the analysed link, Case 2 induces an out-of-plane and in-plane load, while Case 3 is similar to Case 2, apart from an added phase difference between the two angles. The stress and strain results from the finite element analyses are input in the Pragtic fatigue software. For each case, a number of fatigue criteria are calculated. These criteria are, named after the author, the following: McDiarmid, Dang Van, Matake, Liu & Mahadevan, Carpinteri & Spagnoli, Findley, Wang & Brown & Miller, Smith & Watson & Topper and Socie. Different critical plane search algorithms and/or cycle counting methods have been explored. Some of these criteria lead to a Fatigue Index, while others lead to an Accumulated Damage formulation. From the results it is clear that the cases combining two angles lead to higher damages, leading to the believe that the multiaxial behaviour should be taken into account when assessing fatigue damage of mooring chains. Furthermore, it seems that for the different cases, the SWT criterion gives either the highest or the lowest damage. As this is originally a multiaxial parameter, it shows that the use of traditional uniaxial methods could either over- or underestimate the damage, depending on the specific loading. Furthermore, results show that the criterion that is suggested by Bureau Veritas' Guidance Note on OPB, namely the Dang Van criterion, often gives the lowest fatigue index. This suggests that this criterion might not be conservative enough. This statement needs to be validated with the help of experiments. Furthermore, the method specifically aimed at multiaxial problems, the Wang & Brown method (including the multiaxial cycle counting method), leads to highest accumulated damage. As this method was aimed for multiaxial and non-proportional loading, it can be reasoned that this method makes a conservative, proper prediction. As for the critical plane orientation, it seems that the most damaging plane, likely the location of crack growth, is often close to the shear plane. This fuels the believe that the shear stress is the factor driving the OPB failure mode. However, since this problem inherently involves a mean stress (the tension on the mooring chain), the critical plane does not need to be the shear plane. When exploring this with the globe plane search algorithm, it seems that the critical plane is often a plane oriented at some angle in between the shear and normal plane. The results and statements made in this report are at this point mathematical. As the OPB concept is relatively newly discovered, more experiments are needed to be able to back up any statements that can be made. Furthermore, the research presented here could benefit from a larger group of cases, and added detail on the loading part of the analyses. Furthermore, as material fatigue parameters are limited, a sensitivity anayses on these parameters could shed some light on the influence of parameters used. The parameters used in this report are taken from similar materials and should at least give a very reasonable approximation of the material's fatigue behaviour.