A three layer elastic-gravitational fault displacement model has been developed using elastic dislocation and employed to examine the effects of rigidity layering, gravity, and stress relaxation on surface and subsurface displacements fields for a dip-slip normal fault. Within our three layer model, layer 1 represents the upper crust, layer 2 the lower crust, and layer 3 the upper mantle. The fault is embedded in the upper crust. Horizontal as well as vertical displacement components have been determined. Displacement field changes due to postseismic stress relaxation have been calculated using both the correspondence principle and relaxed rigidity moduli, and results are in close agreement. The relaxed rigidity method provides an accurate and computationally efficient method of examining postseismic relaxation. Postseismic relaxation within the lower two layers only, gives surface uplift, increasing footwall uplift and decreasing hangingwall subsidence, and also increases the wavelength of surface vertical displacement. Postseismic stress relaxation within all three layers (i.e., uniform half-space) produces a shorter wavelength of surface vertical deformation with respect to the coseismic response. Moho topography created during coseismic deformation is initially amplified during postseismic relaxation. The relaxed Moho topography is dependent on the strength of the upper crust as well as the strength of the lower crust and mantle. Gravity has a significant influence on displacements only at the postseismic stage when the effective rigidity of the lower layers is small. Coseismic and postseismic normal strains associated with dip-slip normal faulting have been examined. For a large normal basement fault intersecting the free surface, the coseismic horizontal surface strain, perpendicular to fault strike, is compressive adjacent to the fault and in the footwall, and tensile in the hangingwall away from the fault. Coseismic stress redistribution may generate significant tensile brittle failure of the upper crust adjacent to large basement faults. ¿ American Geophysical Union 1995