A computational method is proposed to simulate 3D unsteady cavitating flows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two-phase flow phenomena. The initial model is a time-marching algorithm devoted to compressible flow, associated with a low-speed preconditioner to treat low Mach number flows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating flows. It is based on a barotropic state law that relates the fluid density to the pressure variations. A modification of the preconditioner is proposed to treat efficiently as well highly compressible two-phase flow areas as weakly compressible single-phase flow conditions. The numerical model is applied to time-accurate simulations of cavitating flow in spatial turbopump inducers. The first geometry is a 2D Venturi type section designed to simulate an inducer blade suction side. Results obtained with this simple test case, including the study of its general cavitating behaviour, numerical tests, and precise comparisons with previous experimental measurements inside the cavity, lead to a satisfactory validation of the model. A complete three-dimensional rotating inducer geometry is then considered, and its quasi-static behaviour in cavitating conditions is investigated. Numerical results are compared to experimental measurements and visualizations, and a promising agreement is obtained. Copyright © 2004 John Wiley & Sons, Ltd.