In this Thesis inviscid models based on the Boundary Element Method are developed for the calculation of partial and super sheet cavitation on hydrofoils and marine propellers. The two and three-dimensional, steady and unsteady cases are considered. The model is found to be fast, robust and accurate, hence suitable for the implementation of a cavitation model. A three-dimensional cavitation model without re-meshing is implemented and extensive numerical studies are performed for hydrofoils and propellers. The numerical results for cavitating flow show good agreement with the experimental data for the MARIN S-Propeller and the INSEAN E779A propeller.