Grain shape can introduce anisotropy in creep which depends on the diffusion of vacancies between grain boundary sources and sinks. Such anisotropy is examined to determine the rate of creep under multiaxial stresses both for lattice and grain boundary diffusion. Noting the role of grain boundary sliding in this form of creep it is shown that, with some approximations that only become significant in an identified case, complete and fully self-consistent formulae can be derived for the rate of creep in terms of grain dimensions. The results are presented in the form of compliance matrices which are analogous to those that have a well-established role in the characterization of elastic anisotropy. A comparable usefulness of these `creep compliance coefficients' is envisaged in evaluating anisotropic diffusional creep behaviour and a similar approach can be extended to more general cases where creep rates may be interface controlled.