An analysis is made of viscoelastic lithosphere/asthenosphere coupling in the time-dependent redistribution of stress along plate boundaries or other seismic linements following great earthquakes. the study is based on a generalization by Rice of Elsasser's model of stress-diffusion, in which general elastic plane stress deformations are allowed in lithosphereic plates which are coupled in an elementary way to a (Maxwellian) viscoelastic asthenosphere. Solutions are developed which describe the large-scale quasi-static distribution of thickness-averaged stresses in the lithosphere at or near stationary or traveling rupture zones, modeled here by either crack-like zones of fixed stress drop or dislocationtype slip zones. Sudden ruptures shed load onto the asthenosphere which is gradually transferred back to the lithosphere by a slow relaxation process. The spatial and temporal characteristics of the predicted stress alterations suggest a significant role of lithosphere/asthenosphere coupling effects in triggering interactions of great earthquakes, patterns of prolonged aftershock activity, and the breaking of barriers or gaps by time-dependent stressing.