The Poisson coefficients of a 3D cellular solid are calculated as function of structure characteristics. A significant structural anisotropy is introduced by considering ellipsoid voids where their elongation and orientation are controlled using the random sequential addition (RSA) algorithm. The relative density of the material is varied between 0.1 and 0.3 in order to obtain an open cell structure. Finite element calculation is performed to calculate the six Poisson coefficients of the material. Predicted results show that all quantities are not independent and that three independent coefficient sets can be related to the ratio of the fully oriented ellipsoids and the elongation parameters. No clear correlation can be derived between the Poisson coefficients and the relative density suggesting a fixed-point effect. It seems that some coefficients are more sensitive to the Poisson coefficient of the solid phase, especially under those conditions where the percolation of the solid, in the direction of main alignment, is the largest one.