In this talk we analyze the yield criterion of a porous material containing cylindrical and spherical cavities on the basis of the Gurson mechanical model where the matrix is pressuresensitive. Both limit analysis (LA) methods are used to determine as closely as possible the corresponding macroscopic criterion, by using conic programming formulations. For a Drucker-Prager matrix the case of cylindrical cavities is investigated in generalized plane strain, and the results compared with those of previous works for von Mises matrices. Then we study the case of a Coulomb matrix for spherical cavities under axisymmetrical conditions. Due to the constraining character of the axisymmetry, specific analytical solutions are superimposed on the numerical fields. Among other results, a comparison with an ad hoc translated “modified Cam-Clay criterion” points out that it might be considered as a satisfactory approximation, except that it does not account for the corner of our criterion on the isotropic compressive axis, unlike the original Cam-Clay criterion.