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Given the large energy resource available in ocean waves, wave energy converters have been developed over the last decades for power extraction. Various concepts exist, and research efforts are now focussed on reducing their levelised cost of energy. The device structure has been identified to have the highest cost reduction potential. For this reason, a number of hull geometry optimisation studies have been performed in recent years. In these studies, costs have been mostly represented through the device size or weight, and devices have been optimised for specific sea conditions, based generally on simple shapes such as spheres or cylinders. However, there is no consensus in the employed methodology and resulting shapes might be difficult to manu facture or unable to survive in high energetic seas. The goal of this thesis is, therefore, to develop a device-agnostic methodology for geometry optimisation of wave energy converters, which enables the generation of improved hull shapes that reduce the levelised cost of electricity. An existing approach for single body floating point-absorbers, exhibiting some of the best practices found in this field, is re-implemented and extended to improve its robustness for its application to different case studies. Each of the elements composing this approach (how the geometry is defined, the choice of objective function and the choice of optimisation algorithm and set-up) are then evaluated and their suitability is assessed through comparison to other strategies. The method is then applied to a range of study cases, such as to study the effect of location and of the choice of modes-of-motion for power extraction on the optimal hull shape. Further extensions of the method to include manufacturability and reliability considerations, as well as to include the effect of mass distribution are investigated. As a result, recommendations are formulated for the set-up of an early stage WEC design geometry optimisation process. Additionally, trends for the hull shape design are identified for the considered cases - depending on, location, the choice of the modes of motion for power extraction, and how costs are accounted for.