Numerical models employing the fully nonlinear potential flow theory have been studied for over three decades. Adopting the mixed Eulerian–Lagrangian formulation, solution over the fluid domain has been obtained using both the boundary integral/element and finite-element (FE) methods, the latter being the main focus of the present paper. The FE model is derived employing a variational formulation. The main highlight of the FE model developed pertains to the calculation of fluid particle velocities using a C0-type FE solution. The velocity calculation procedure is analogous to the traditional stress calculation approach used in FE analysis of solid mechanics problems and is applicable to unstructured isoparametric hexahedral meshes. The numerical model has been applied to evaluate nonlinear diffraction forces on single cylinder problems and Fourier decomposition has been applied to the pressure force time history obtained. The first-order diffraction forces and moments derived from the present nonlinear model compare very well with literature results. The second-order oscillating and mean forces as well as the second-order mean moments compare fairly well with literature results. However, significant deviations are seen in the second-order oscillating moments. It is conjectured that side wall reflections of higher-order wave components in the numerical wave tank might be responsible for this. This aspect merits further investigation. © 2016 Informa UK Limited, trading as Taylor & Francis Group.