A model of damage evolution in austenitic stainless steels under creep loading at elevated temperatures is proposed. The initial microstructure is idealized as a space-tiling aggregate of identical rhombic dodecahedral grains, which undergo power-law creep deformation. Damage evolution in the form of cavitation and wedge cracking on grain-boundary facets is considered. Both diffusion and deformation-driven grain-boundary cavity growth are treated. Cavity and wedge-crack length evolution are derived from an energy balance argument that combines and extends the models of Cottrell (1961 Trans. AIME 212 191-203), Williams (1967 Phil. Mag. 15 1289-91) and Evans (1971 Phil Mag. 23 1101-12). The time to rupture predicted by the model is in good agreement with published experimental data for a type 316 austenitic stainless steel under uniaxial creep loading. Deformation and damage evolution at the microscale predicted by the present model are also discussed. © 2011 IOP Publishing Ltd.