Technologies for harvesting offshore renewable energy based on float- ing platforms, such as offshore wind, wave and tidal energies, are currently being developed with the purpose of achieving a competitive cost of energy. The eco- nomic impact of the mooring system is significant within the total cost of such deployments, and large efforts are being carried out to optimize designs. Analysis of mooring systems at early stages generally require a trade-off between quick analysis methods and accuracy to carry out multi-variate sensitivity analyses. Even though the most accurate approaches are based on the non-linear finite ele- ment method in the time domain, these can result in being very time consuming. The most widely used numerical approaches for mooring line load estimates are introduced and discussed in this paper. It is verified that accurate line tension estimates require lines drag and inertia forces to be accounted for. A mooring and floating structure coupled model based on the lumped mass finite element ap- proach is also discussed, and it is confirmed that the differences found in the coupled numerical model are mainly produced by the uncertainty on hydrody- namic force estimates on the floating structure rather than by the lumped mass method. In order to enable quick line tension estimates, a linearization of the structure and mooring coupled model is discussed. It shows accurate results in operational conditions and enables modal analysis of the coupled system.