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SUMMARYA numerical model is presented for the simulation of complex uid ows with free surfaces in three space dimensions. The model described in Maronnier et al. (J. Comput. Phys. 1999; 155(2):439) is extended to three dimensional situations. The mathematical formulation of the model is similar to that of the volume of uid (VOF) method, but the numerical procedures are di erent.A splitting method is used for the time discretization. At each time step, two advection problemsone for the predicted velocity ÿeld and the other for the volume fraction of liquid-are to be solved. Then, a generalized Stokes problem is solved and the velocity ÿeld is corrected. Two di erent grids are used for the space discretization. The two advection problems are solved on a ÿxed, structured grid made out of small cubic cells, using a forward characteristic method. The generalized Stokes problem is solved using continuous, piecewise linear stabilized ÿnite elements on a ÿxed, unstructured mesh of tetrahedrons.The three-dimensional implementation is discussed. E cient postprocessing algorithms enhance the quality of the numerical solution. A hierarchical data structure reduces memory requirements.Numerical results are presented for complex geometries arising in mold ÿlling.