The present thesis considers numerical computations of fully nonlinear fluid-structure interaction. The aim of the thesis is to establish a well validated fully nonlinear numerical wave tank for the simulations of complex fluid-structure interaction of moored floating offshore structures. The numerical computations are carried out using the fully nonlinear numerical fluid-structure interaction solvers, interFoam and interDyMFoam, from the open-source CFD libraryOpenFOAM®. These solvers make use of a fully nonlinearNavier-Stokes/VOF solver for the computations of the two-phase flow field, where the interDyMFoam solver also utilises a 6-DOF motion solver to compute the motions of the floating structure. These solvers were extended with waves2Foam, a wave generation and absorption toolbox, developed by Jacobsen et al. (2012). The extended interFoam and interDyMFoam solvers, hereafter referred to as the waveFoam and interDyMFoam solver, were utilised for the computations of fluid-structure with fixed and moving structures respectively. Furthermore, an implementation of catenary mooring lines is provided by Niels Jacobsen (Researcher/advisor at Deltares), for the simulations of the mooring system of the floating structure. Finally, the fully nonlinear potential flow solver, OceanWave3D, was utilised in a fully nonlinear and fully parallelised domain decomposed solver, developed by Paulsen (2013) and Paulsen et al. (2014b), for the efficient computations of realistic sea states. Here, the outer wave field is described by the potential flow solver, whereas the inner wave field, in the vicinity of a given structure, is described by the interDyMFoam solver. The waveFoam and waveDyMFoam solvers are carefully validated either in terms of convergence by grid refinement or by comparisons to experimental measurements. Special attention is paid to the waveDyMFoam solver with respect to the computation of the flow induced motions of a moored floating wind turbine. The ability of the numerical model to accurately reproduce experiments, performed with the generic OC5 floating wind turbine model in the MARIN Concept Basin, is also investigated. The Navier-Stokes/VOF basedwaveFoam andwaveDyMFoam solvers were evaluated with respect to wave propagation and wave structure interaction in a two-dimensional set-up. A grid convergence study was performed on the propagation of a fully nonlinear stream function wave. The convergence rate of the two-phase numerical solution to the single-phase stream function solution was verified. Successful computation of wave loading on a partially submerged fixed horizontal cylinder was provided. The accuracy of the numerical model, with respect to fluid-structure interaction for free and forced motion of a structure, was verified with the generation of surface waves by the forced oscillation and the free heave decay of a horizontal cylinder. These two-dimensional cases were also used to verify the efficiency of two meshing tools, provided by the OpenFOAM® toolbox. These meshing tools were shown to provide excellent results, and more importantly, provided a less complicated method for generating surface boundary meshes of complex three-dimensional structures. The waveDyMFoam solver is used for the computation of free and moored decay test of the three-dimensional floating wind turbine model. The accuracy of the numerical solution was verified against numerical computations from the work of Dunbar et al. (2015) and physical experiments performed at MARIN. Finally, a proof-of-concept case is performed, involving the modelling of a three-dimensional moored floating wind turbine subjected to irregular uni-directional waves. In these numerical computations, the potential of the waveDyMFoam and the domain decomposition strategy are evaluated.