Ductile fracture of materials occurs by nucleation, growth and coalescence of microvoids. The most classical model describing the voids growth in plastic porous materials is introduced by Gurson. This model was derived from limit-analysis of a hollow sphere subjected to conditions of homogeneous boundary strain rate. Gurson's model was extended to spheroidal, both prolate and oblate voids by Gologanu et al. In this work, we further extend Gologanu et al's model to general ellipsoidal voids. In a first step, the velocity field satisfying conditions of homogenous strain rate on all ellipsoids confocal with the void and the outer boundary, discovered by Leblond and Gologanu, is used in a limit-analysis of an ellipsoidal domain. A Gurson-like approximate yield function is obtained. In a second step, the preceding limit-analysis is improved: (i) For hydrostatic loadings, by performing micromechanical finite element computations in a number of significant cases; (ii) For deviatoric loadings, by directly using some general rigorous results for nonlinear composites. In a third step, the yield function proposed is validated versus a number of numerical computations of yield surfaces of hollow cells of various ellipsoidal shapes. In a fourth step, suitable evolution equations for the shape and orientation of the voids in plastic material are defined. The last step is devoted to the implementation of the Hill's criterion in SYSTUS software and makes it possible to consider the extension of the model to plastic anisotropic materials
