This paper addresses the mathematical modelling of the relationship between the free surface elevation (FSE) and the excitation force for wave energy devices (excitation force model). While most studies focus on the model relating the FSE to the device motion, the excitation force model is required to complete the mathematical wave energy system description and also plays an important role in excitation force observer design. In the paper, a range of linear and nonlinear modelling methodologies, based on system identification from numerical wave tank tests, are developed for a range of device geometries. The results demonstrate a significant benefit in adopting a nonlinear parameterisation and show that models are heavily dependent on incident wave amplitude.