Most wave energy converters (WECs) are described by linear mathematical models, based on the main assumption of small amplitudes of motion. Notwithstanding the computational convenience, linear models can become inaccurate when large motions occur. On the other hand, nonlinear models are often time consuming to simulate, while model-based controllers require system dynamic models which can execute in real time. Therefore, this paper proposes a computationally efficient representation of nonlinear static and dynamic Froude–Krylov forces, valid for any heaving axisymmetric point absorber. Nonlinearities are increased by nonuniform WEC cross sectional area and large displacements induced by energy maximising control strategies, which prevent the device from behaving as a wave follower. Results also show that the power production assessment realized through a linear model can be overly optimistic and control parameters calculations should also reflect the true nonlinear nature of the WEC model.