This paper presents recent numerical studies conducted at The University of Edinburgh related to a modified version of the Edinburgh duck wave energy converter. Its purpose is seawater desalination rather than electricity production, but under the assumptions taken the results can be applied to both versions. From the design point of view, the key innovation is the change of the shape of the device. Wave energy can be converted into useful work by the same pitching motion by means of a circular cylinder with an offset axis of rotation without the front beak, allowing significant cost reduction. The results to be presented were obtained using the Boundary Element Method (BEM) package WAMIT, based on linear wave theory. The hydrodynamic behaviour of the device is assessed, allowing comparisons with experimental work on a 1:33 scale model. Full-scale figures are also presented. The influences of both the position of the axis of rotation and the submergence ratio are evaluated. A total of ten different configurations, each for two different submergence ratios, are analyzed. Focus is given to the hydrodynamic coefficients, the wave exciting force, the response amplitude operator (body motions), and the relative capture width.