We present a theoretical treatment of the effect of stress on dopant and defect diffusion in Si. A prior treatment [P.H. Dederichs and K. Schroeder, Phys. Rev. B 17, 2524 (1978)] of vacancy diffusion in strained fcc metals is extended to include more general defects and crystallinity. The new method is applied to Jahn-Teller distorted vacancies in Si, which we predict to show isotropic diffusion for (100) grown uniaxially strained films, but strong anisotropic diffusion for (111) films.