A large-strain elastoplastic analysis is presented for a cylindrical cavity embedded in an infinite medium under uniform radial pressure. The investigation employs invariant, non-associated deformation-type theories for Mohr-Coulomb (M-C) and Drucker-Prager (D-P) solids, accounting for arbitrary hardening, with the equivalent stress as the independent variable. The M-C model results in a single first-order differential equation, whereas for the D-P solid an algebraic constraint supplements the governing differential equation. Material parameters and response characteristics were determined by calibrating the models with data from triaxial compression tests on Castlegate sandstone and on Jurassic shale. A comparison is presented between predictions obtained from the two models and experimental data from hollow cylinder tests under external loading. A sensitivity of the results to material parameters, like friction and dilation angles, is provided for the case of a cavity subjected to internal pressure in terms of limit pressure predictions. In all cases it has been found that the results of the D-P inner cone model are in close agreement with those obtained from the M-C model.