High accuracy at a low computational time is likely to be a fundamental trait for mathematical models for wave energy converters, in order to be effective tools for reliable motion prediction and power production assessment, device and controller design, and loads estimation. Wave energy converters are particularly prone to exhibit complex and nonlinear behaviours, which are difficult to be modelled efficiently. Highlynonlinear effects, related to nonlinear Froude-Krylov forces, are nonlinear coupling, instability, and parametric resonance, which may damage or improve the power production. It is therefore fundamental to be able to describe such nonlinearities, in order to assess their repercussion on the performance of the device, and eventually design the system in order to exploit them. This paper provides a computationally efficient, compact, and flexible modelling approach for describing nonlinear Froude- Krylov forces for axisymmetric wave energy devices, in 6 degrees of freedom. Unlike other similar models, based on a mesh discretization of the geometry, the analytical formulation of the wetted surface allows the dynamical model to run almost in real time.