SUMMARYA computational method is proposed to simulate 3D unsteady cavitating ows in spatial turbopump inducers. It is based on the code FineTurbo, adapted to take into account two-phase ow phenomena. The initial model is a time-marching algorithm devoted to compressible ow, associated with a lowspeed preconditioner to treat low Mach number ows. The presented work covers the 3D implementation of a physical model developed in LEGI for several years to simulate 2D unsteady cavitating ows. It is based on a barotropic state law that relates the uid density to the pressure variations. A modiÿcation of the preconditioner is proposed to treat e ciently as well highly compressible two-phase ow areas as weakly compressible single-phase ow conditions. The numerical model is applied to time-accurate simulations of cavitating ow in spatial turbopump inducers. The ÿrst 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.