We extend a technique previously used to model surface displacements resulting from thrust faulting in an elastic-gravitational layer over a viscoelastic-gravitational half-space to the case of strike-slip faulting. The method involves the calculation of the Green's functions for a strike-slip point source contained in an elastic-gravitational layer over a viscoelastic-gravitational half-space. The correspondence principle of linear viscoelasticity is applied to introduce time dependence. The resulting Green's functions are then integrated over the source region to obtain the near-field displacements. Several sample calculations are presented involving 90¿ and 30¿ dipping faults and ruptures completely and partially through the elastic layer. We also illustrate the time dependent deformation due to a buried fault. Results show that the use of a viscoelastic half-space underlying an elastic layer introduces a long wavelength component into the deformation field <Cohen and Kramer, 1984>, even in cases of non vertical strike-slip fault and inclusion of gravitational effect, that cannot be modeled by purely elastic techniques. Calculations have shown that vertical postseismic displacement is insignificant and that the horizontal movement is about the same magnitude as the coseismic strike-slip displacement. The inclusion of gravity affects the horizontal displacement due to vertical strike-slip faulting in far field and the vertical displacement for dipping strike-slip faulting in near-field. The computed results have been fit to the Global Positioning System measurements of the Landers earthquake taken shortly after the main shock, assuming a relaxation time of the order of days. This relaxation time is considerably shorter than times of the order of years to decades found in previous studies. The major differences between this detailed three-dimensional and simplified two-dimensional model are the decay of magnitude in displacement field and the distinct displacement pattern in the regions beyond the fault tip. The displacement field due to the cyclic earthquakes was constructed by considering the finite fault length and inclusion of gravity. It is found that the displacement field is dominated by the plate motion in the case of short recurrence time. On the other hand, a ''looping'' and migrating pattern in the displacement field is found in the case of very long recurrence time, which is not seen in those 2D simplified models. ¿ American Geophysical Union 1996