Fault motion during a dip-slip earthquake induced elastic stresses in the earth which are well modeled by elastic dislocation theory. Shortly after the earthquake, flow in the asthenosphere begins to relax these stresses and leads to postseismic motions observable at the earth's surface. Recent work has led to apparently contradictory results on the sign of the vertical motion following a dip-slip earthquake: some workers find downwarping in the region overlying a thrust fault; others find upwarping. This controversy is now resolved by a finite element study of postseismic rebound following a thrust earthquake on a 30¿ dip fault in an initially planar elastic lithosphere which overlies a Maxwell viscoelastic asthenosphere. If the fault penetrates less than 0.68 of the way through the lithosphere, downwarping follows the earthquake. If the fault penetrates more than 0.68 of the lithosphere, upwarping results. The magnitude as well as the sign of the postseismic rebound is a sensitive indicator of the ratio between the thickness of the elastic lithosphere and the fault depth. Observations of postseismic rebound may thus be used to measure lithosphere thicknesses at time scales on the order of years.