It is essential that floating offshore vessels have fit-for-purpose mooring systems. The mooring system consists of freely hanging lines connecting the surface platform to anchors, or piles, on the seabed, positioned at some distance from the platform. The mooring lines are laid out, often symmetrically in plan view, around the vessel. Steel-linked chain and wire rope have conventionally been used for mooring floating platforms. Each of the lines forms a catenary shape, relying on an increase or decrease in line tension as it lifts off or settles on the seabed, to produce a restoring force as the surface platform is displaced by the environment. A spread of mooring lines thus generates a non-linear restoring force to provide the station-keeping function. The force increases with vessel horizontal offset and balances quasi-steady environmental loads on the surface platform. The equivalent restoring stiffness provided by the mooring is generally too small to influence wave frequency motions of the vessel significantly, although excitation by low-frequency drift forces can induce dynamic magnification in the platform horizontal motions and lead to high peak line tensions. The longitudinal and transverse motions of the mooring lines themselves can also influence the vessel response through line dynamics. With the requirement to operate in increasing water depths, the suspended weight of mooring lines becomes a prohibitive factor. In particular, steel chains become less attractive at great water depths. Recently, advances in taut synthetic fibre rope technology have been achieved offering alternatives for deep-water mooring. Mooring systems using taut fibre ropes have been designed and installed to reduce mooring line length, mean- and low-frequency platform offsets, fairlead tension and thus the total mooring cost. To date however, limited experience has been gained in their extended use offshore when compared to the traditional catenary moorings.