A viscous flow model of a subduction zone is used to calculate the near-trench deformation and topography of the overriding plate in response to tectonic and buoyancy forces. The tectonic force, which is associated with global plate motion, arises from subduction of a cold oceanic lithosphere that shears the overriding lithosphere along the contact between the two plates. The buoyancy force arises in response to horizontal density variations and tends to relax the existing topography. The time evolution of the near-trench topography is investigated via a finite element technique that solves for the flow field in the overriding plate. The results indicate that the near-trench topography approaches a steady state configuration, in which the upper surface topography produces a buoyancy force that balances the tectonic force induced by the subducting slab. The model predicts that the steady state trench depth increases with the subduction rate, and hence explains the correlation between trench depth and subduction rate observed by Grellet and Dubois (1982). Transition from one steady state trench topography to another adds or removes material from the overriding plate; this may result from a change in subduction rate, angle of subduction, or subduction of a seamount. During a transition to a deeper steady state configuration, the near-trench stress field has an extensional component, which agrees with the observed extension in regions of tectonic erosion. Similarly, during a transition to a shallower steady state configuration, the near-trench stress field has a compressional component, which agrees with the observed compression of accretionary wedges. Hence, the model explains tectonic erosion and accretion at trenches as transitional features that indicate a change from one steady state configuration to another. ¿ American Geophysical Union 1992