This study addresses the possibility of extracting energy from gravity waves for marine propulsion by an oscillating hydrofoil. Moreover, it investigates theoretical and numerical methods to achieve modelling of active oscillating wave thrusters. The first part of this work presents a semi-analytical model based on an extension of classical theory of a 2D unsteady hydrofoil, with large oscillations, in waves, including free-surface effects. The second part investigates the same problem with numerical modelling using a CFD solver. Specifically, a deforming grid method is used for body motion modelling, enabling the simulation of cases with large forced motions. The results of the semi-analytical model for mean thrust and propulsive efficiency are compared with published numerical and experimental data, with fair-to-good agreement. The results of CFD simulations for 2D and 3D test cases are investigated, allowing physical interpretation of flow dynamics and forces. Preliminary comparisons with published numerical and experimental results show a promising good agreement. The overall results suggest that the semi-analytical model may prove its usefulness in preliminary design studies, and the CFD model showed itself to be a tool capable of delivering more accurate results for the most complex cases and providing a comprehensive understanding of the flow dynamics.