The paper describes a (FLAC) numerical analysis of the response of cavities of elliptical shape in isotropic elastic perfectly-plastic materials when subjected to non-hydrostatic external stresses and uniform internal pressure. Cases in which the plastic zone completely surrounds the cavity are considered. The material is assumed to obey a Mohr-Coulomb yield condition and the associated flow rule. The extension and shape of the plastic region and the amount of convergence occurring at the wall have been determined using FLAC. Results are compared with those for an equivalent circular cavity under hydrostatic and non-hydrostatic loading. The comparison provides insight on the appropriate orientation of elliptical and similar non-circular cavities (with respect to the directions of the far-field stresses) to minimize the size of the plastic failure region and the resulting convergence.