The hydrodynamic properties of a horizontal cylinder which is free to pitch about an off-centred axis are studied and used to derive the equations of motion of a wave energy converter which extracts energy from incoming sea waves with a linear power-take-off mechanism. The present work follows from a recent study which compared the performance of an off-centred cylinder with those of the Edinburgh Duck wave energy converter. The small decrease in performance found is offset by a reduction in the likely costs associated with the manufacturing of the cylindrical cam compared with those of the asymmetric profile. As part of the survivability strategy in very energetic seas-states it had been planned to completely submerge the device so as to reduce the mooring forces. However, experiments with scale models show that a good absorption capacity is retained even when fully-submerged. The hydrodynamic properties of a horizontal cylinder that pierces the free-surface and of one that is fully submerged are therefore of central concern in this study. These properties are well known for the case of very long cylinders but they are now found for cylinders with different widths, drafts, submergence levels and water-depths. The hydrodynamic forces and moments at the off-centred axis are, furthermore, derived through the application of transformation formulae. The equation of motion of the off-centred cylinder is derived for one degree of freedom and its performance as a wave energy converter is analysed. A relationship which relates the resonance of the device with the location of the off-centred axis and its mass distribution is derived and used to optimize the design for average sea conditions attained at a real location. Design cases associated with three diameters of the cylinder are looked into detail for both a fully-submerged and free-surface piercing cylinder. The one degree of freedom model is extended to include a multi-body which has three degrees of freedom in order to describe the dynamics of a proposed wave powered desalination system based on a cylindrical Duck device. This mathematical model is derived through linearised Lagrangian equations of motion in which the hydrodynamic forces are included as generalised external forces. The advantage of such approach is to reduce the number of equations associated with multi-body systems by removing the reaction forces of holomonic constraints from the system of equations to solve. This model is validated through experiments with a scale model performed in the curved tank of the University of Edinburgh with both regular waves and mixed seas.