The boundary-element method has been widely used as a design tool in the offshore and ship building industry for more than 30 years. Its application to wave energy conversion is, however, more recent. This paper deals with the numerical modelling of a free-floating sloped wave energy device. The power take-off mechanism of the device consists of an immersed tube with a piston sliding inside. The modelling is done using the boundary-element method package WAMIT. The model is first worked out for the case where the axis of the tube is vertical. It is then derived for the tube inclined and successfully verified against numerical benchmark data. A companion paper presents results of a detailed comparison with a physical model study.