The deformation of the earth following a dip-slip earthquake is calculated by using a three-layer rheological model and finite element techniques. The three layers are an elastic upper lithosphere, a standard linear solid lower lithosphere, and a Maxwell viscoelastic asthenosphere. Attention is focused on the magnitude of the postseismic subsidence and the width of the subsidence zone that develops due to the viscoelastic response to coseismic reverse slip. Detailed analysis for a fault extending from the surface to 15 km with a 45¿ dip reveals that postseismic subsidence is sensitive to the depth to the asthenosphere but is only weakly dependent on lower lithosphere depth. The greatest subsidence occurs when the elastic lithosphere is about 30 km thick, and the asthenosphere lies just below this layer (asthenosphere depth =2 times the fault depth). The extremum in the subsidence pattern occurs at about 5 km from the surface break of the fault and lies over the slip plane. At this location the subsidence reaches 60% of the coseismic uplift about 30 Maxwell times. Unlike the horizontal deformation following a strike-slip earthquake, significant vertical deformation due to asthenosphere flow persists for many times the Maxwell time of the asthenosphere. As a consequence, the relaxation of the lower lithosphere has only a secondary effect on uplift and subsidence; it does, however, substantially increase horizontal straining. The width of the postseismic subsidence zone also depends strongly on the depth to the asthenosphere and shows little senstivity to the presence of a slowly relaxing lower lithosphere. Parametric adjustment of the lithosphere thickness and fault dip angle over a considerable range of values in a single model of an elastic lithosphere and viscoelastic asthenosphere reveals that the postseismic subsidence is greatest when the fault penetrates through about one half the lithosphere. Previous estimates of the asthenosphere viscosity (~1019 Pa s) and lithosphere thickness (~30--40 km) for the region of Japan affected by the 1896 Riku-u earthquake are confirmed by model calculations.