In this paper a finite array of hinged flap-type wave energy converters are modelled using a mathematical approach. These are illustrative of the Oyster device of Aquamarine Power Ltd novel semi-analytic solution method is presented for a set of boundary-value problems involving the scattering and radiation of waves by thin barriers used to model the device hydrodynamics. The approach makes use of the geometry to apply Fourier transforms, deriving non-singular integral equations in terms of the jumps in pressure across the flaps. These are then solved numerically using a highly efficient Galerkin expansion method. The focus of the results is on optimisation. We suggest optimal parameters for a single device, highlighting key features of its success and identifying flap length as crucial to device performance. This optimisation is then carried through to arrays with optimal arrangements and spacings being determined for a model sea state. Here, the lateral displacement of the devices emerges as a critical factor in optimal array configuration.