A systematic theoretical and computational study is presented for the diffusion of point defects in a stressed cubic lattice. The study combines an atomistic description of point defect migration with a continuum model for point defect transport. Moment analysis of the macroscale transport equation gives expressions for the drift velocity and the diffusivity tensor of the point defects, which are calculated by a dynamic Monte Carlo simulation of the defect migration process. Results are presented for the case of diffusion under a constant force of interaction between the applied stress on the crystal and the defects. The continuum model gives the general constitutive model for stress-assisted point defect diffusion.