Nowadays, the Norwegian Public Roads Administration plans to replace the ferry connections along the western coast of Norway with fixed road connections through the coastal highway E39 project. Due to the necessity of bridging long distances with considerable depths, non-conventional engineering solutions are being developed. To date, the first fjord planned to be cross is Bjørnafjord, located just in the middle of Trondheim and Kristiansand. In order to bridge the fjord distance, three innovative solutions have been developed: a submerged floating tube bridge, a floating pontoon bridge, and finally, a multi-span suspension bridge. It is known that these structures are affected by periodic environmental forces which may cause significant fatigue problems in some structural components, disturbing their service behaviour. The aim of this master thesis is to deeply analyse the cumulative fatigue damage produced in the mooring lines of a proposed solution for crossing Bjørnafjorden as well as to investigate the influence of the implementation of different mooring line scenarios on the damage. A 3D finite element model of the chosen alternative was conducted and verified. The model provided the stress variations in each mooring line which were processed through Excel software using macros performed as well as Matlab scripts in order to obtain the results. Then, a deep fatigue damage assessment was carried out discussing how different tension-history time period calculations affect to the damage, as well as which fatigue evaluation methodology is adequate for the chosen solution. Moreover, the fatigue damage produced on the initial mooring line system configuration was analysed. It was investigated the repercussions of each direction and the contribution of each environmental load on the total damage. Last but not least, it was researched the influence of different water depths and line configurations on the fatigue damage. The results show that the fatigue damage obtained for the adopted solution remains far from the failure threshold with the worst damage produced in the mooring line chain components. The previous results have been computed employing a 1-hour analysis duration through the rainflow counting method. Also, the worst fatigue damage is produced by environmental states propagating in a westerly direction, corresponding to the maximum fetch. Regarding the load contribution in the fatigue damage, it is proved in this case that the current loads stabilise the mooring lines, reducing the fatigue damage. Finally, investigating the effect of various mooring line scenarios on the damage it has been proved that the fatigue damage is increased as the water depth is decreased and as the lateral mooring lines are separated from the initial configuration.