A model is developed for creep crack growth in which a grain boundary cavity grows by boundary diffusion ahead of a main crack. The cavity can be either cylindrical or crack-like in shape, and growth rates are calculated for both geometries, as well as the conditions under which each is found. Surface and grain boundary diffusion are linked in the model. While both geometries result in a fourth power dependence on the nominal stress intensity (K) for low values of K, this dependence weakens (towards K**2) for crack-like cavities at higher K. Experimental evidence for both creep cracking and creep fracture supports the model.