The paper presents a study of using a modified k-ω model to predict the unsteady cavitating flows around 2D and 3D hydrofoils in the framework of multi-phase mixture flow RANS approach. The cavitation is modeled by Schnerr-Sauer’s cavitation model. A 2D NACA0015 foil at cavitation number σ=1.0 (unsteady with cloud shedding) is studied first, followed by the Delft twisted 3D foil. It is found that the present RANS method is able to predict the essential features like re-entrant jets, the periodic shearing and shedding of cloud cavities. Two distinct shedding dynamics are noted for the 2D foil: (a) Shedding of medium to large scale structures (at low frequency); (b) Shedding of a series of secondary vortex cavities (at high frequency). For the 3D twisted foil, the collaborated effect of re-entrant jets from the curved closure line to break up a primary cavity, as well as the formation, roll-up and transport of cavitation vortices that are observed in the experiment are truly reproduced in the simulation. The method is found to have a tendency to under-predict the lift coefficients.