A semi-analytic elastoplastic model predicting the onset of failure in wellbores subjected to in-situ stress and pore pressure fields is presented. The model also has sanding applications. Rock elastic behaviour is modelled as being linear, with the plastic response described by a non-associated Mohr-Coulomb strain hardening deformation theory. The pore pressure gradient is taken into account using a source solution at the wellbore. Constitutive relations are calibrated using triaxial tests on Castlegate Sandstone cores. Hollow cylinder experiments, again performed with Castlegate sandstone, are used to evaluate predictions. Numerical examples illustrate how constitutive parameters influence the stress state around the wellbore and the onset of failure.