This paper reports on a viscoelastic model for deformation and stress associated with earthquakes. The model consists of a rectangular dislocation (strike slip fault) in a viscoelastic layer (lithosphere) lying over a viscoelastic half space (asthenosphere). The first part of the paper contains an analysis of the time-dependent surface stresses. The model predicts that near the fault a significant fraction of the stress that was reduced during the earthquake may be recovered by viscoelastic softening of the lithosphere. By contrast, the strain shows very little change near the fault. The model also predicts that the stress changes associated with asthenospheric flow extend over a broader region that those associated with lithospheric relaxation, even though the peak value is less. The second part of the paper studies the dependence of the displacements, strains, and stresses on fault parameters. Peak values of strain and stress drop increase with increasing fault height and decrease relatively insensitive to fault depth.