Convective flow within the interiors of terrestrial planets is a primary source of large-scale topographic and tectonic features. We treat the crust and mantle as a layered viscous half-space and find solutions for flow driven by a buoyancy force distribution within the mantle and by relief at the surface and crust-mantle boundary. The crust initially responds to mantle upwelling with uplift, but coninued flow causes significant crustal thinning and subsidence. Downwelling leads to initial subsidence and subsequent crustal thickening and surface uplift. Changes in crustal thickness are driven by (1) vertical normal stresses due to mantle flow and (2) shear coupling of horizontal mantle flow into the crust. The degree and time scale of crustal deformation are sensitive to crustal thickness and viscosity and the presence of elastic layers in the upper crust and mantle. Deformation can occur on time scales less than several hundred million years for resonable values of these parameters. Strong or elastic upper crustal layers enhance crustal thinning or thickening, while large viscosity contrasts between the lower crust and upper mantle or elastic mantle layers tend to diminish deformation. For time-dependent mantle flow due to a rising or sinking diapiric body, crystal deformation depends upon the ratio of diapir radius to crustal thickness, and the ratio of crystal to mantle viscosity. A sinking diapir can lead to crustal thickening, elevated topography, and a specific sequence of time-varying deformation. While regions such as Beta Regio have long been suggested to result from convective upwelling in the Venus mantle, we suggest that a mantle downwelling origin is consistent with many of the characteristics of the compressional mountain ranges of western Ishtar Terra. ¿ American Geophysical Union 1990