This paper concerns the modelling of the wave energy absorbing qualities of a three-dimensional hinged flap-type wave energy converter closely related to the Oyster device. An analytic approach is taken to solving a set of boundary-value problems which arise from the decomposition of the linear water wave problem describing the interaction of the flap converter with waves into scattering and radiation potential problems. A novel integral equation formulation and numerical solution for approximating the solution of these boundary-value problems involving fixed and radiating thin barriers is also presented. Results concentrate on parameters likely to be close to those representing the Oyster device and attempt to expose features of Oyster that make it a successful wave energy absorber, despite theoretical results suggesting otherwise. Amongst the conclusions, it is shown that the length of flap is crucial in determining the optimal performance of the device.