Floating structures are complex systems composed of superstructure, floating-mooring components, and anchors. In this study, the behaviours of a pontoon, which is used as a floating structure, and four mooring elements under different wave loading conditions were investigated. A numerical analysis of the coupled motions of the pontoon, mooring lines, and marine environment was performed. While the mooring lines were modelled as wire elements, the pontoon was modelled as a rigid body with six degrees of freedom. Wave loading conditions were represented using two different wave spectra. The first spectrum (Case I) was generated based on a single sinusoidal wave utilising the JONSWAP spectrum, whereas the second one (Case II) was generated based a superimposed multi-sinusoidal wave. Time-varying motions of the pontoon and tensions of the mooring lines were determined based on the numerical analyses for Cases I and II. Critical values were determined using the results of both cases. The numerical solutions were based on bidirectional fluid–structure interaction (FSI) analysis. A fully non-linear free surface simulation was performed using the coupled Eulerian–Lagrangian (CEL) technique. Furthermore, numerical results were compared with the results obtained from analytical solutions of free surface elevations.