When carrying out any numerical modelling it is useful to have an analytical approximation available to provide a check on the accuracy of the numerical results and to give insight into the underlying physics of the system. The numerical modelling of wave energy converters is an efficient and inexpensive method of undertaking initial optimisation and experimentation. Therefore, the main objective of this paper is to determine an analytical approximation for the wave excitation forces on a floating truncated vertical cylinder in water of infinite depth. The approximation is developed by solving appropriate boundary value problems using the method of separation of variables. A graphical representation of the analytical approximation for the truncated vertical cylinder and the cylinder of infinite depth are presented and are compared to the results from a computational fluid dynamics analysis, using a commercial boundary element package. The presented analytical approximation and the computational fluid dynamics analysis results were found to be in good agreement. Furthermore, the presented analytical approximation was found to be in good agreement with independent experimental data.