In this work it is shown that the exact plastic potential for porous solids with von Mises perfectly plastic matrix containing spherical cavities should involve a very specific coupling between the mean stress and the third invariant of the stress deviator. Furthermore, a new approximate plastic potential that preserves this key feature of the exact one is developed. Unlike all existing analytical criteria for porous solids with von Mises matrix, this new criterion displays a lack of symmetry with respect to both the hydrostatic and deviatoric axes. A full-field approach is also used to generate numerical gauge surfaces. These calculations confirm the aforementioned new features of the dilatational response.