An explanation of the dimensional instability of alpha-uranium under irradiation is advanced, based upon the anisotropic diffusion of lattice imperfections to grain boundaries and free surfaces. An approximate solution of the diffusion equations for an ellipsoidal grain is obtained, which predicts growth rate as a function of pile flux, temperature, and grain size. The calculations are applied to polycrystalline material and some comparisons made between theory and experiment, which confirm the feasibility of the suggested mechanism of dimensional instability.