Large-scale continental tectonics of back arc (extentional) and Andean-type (compressional) environments are investigated by using the thin viscous sheet model to calculated the deformation within continental lithosphere that is subjected to horizontal forces on its plate boundaries and to basal drag from the asthenospheric flow beneath. The shear tractions acting on the base of a deformable lithosphere are derived from a corner flow model that assumes a rigid subducting plate and a deformable overlying plate. Because the calculated shear tractions and the deformation within the overlying plate are interdependent, the corner flow and the thin viscous sheet models are solved simultaneously. We use a perturbation method to obtain analytical solutions for the velocity and strain rate fields within the overlying continental lithosphere. The solutions depend on the angle of subduction, the dimensionless thickness of the lithosphere, and the ratio of asthenospheric to lithospheric viscosities, which governs the viscous coupling between the asthenosphere and the lightosphere. Calculations are compared with observations from the Andes and the Aegean; our results explain some of the features of the deformation in these regions that have heretofore not been explained by other models. Our model predicts that in a compressional environment a broad region of uplifted topography will tend to develop above a more steeply dipping slab (30¿), rather than above a shallower slab (10¿--15¿); this is in accord with observations in the various segments of the central Andes. For an extensional environment, the model predicts that a zone of compression can develop near the trench and that extensional strain rate can increase with distance from the trench, as is observed in the Aegean. We also estimate the effective viscosities of ~1020 Pa s for the asthenosphere, ~2¿1021 Pa s for the Aegean lithosphere, and ~1022 Pa s for the Andean lithosphere. ¿ American Geophysical Union 1989