The quasi static time-dependent behavior after strike slip earthquakes is studied using three-dimensional finite-element models. The effects of lateral heterogeneities, finite fault, and nonuniform fault slip are included. Models of a great earthquake and a medium size earthquake are constructed using a set of possible viscosity structures. Deformation change after an earthquake is found to be sensitive to the viscosity structure located beneath the fault zone. The presence of low viscosity beneath the fault concentrates the horizonal displacement near the fault zone and completely changes the character of vertical deformation. Thus leveling, in addition to horizontal geodetic measurements after a strike slip event, is important in determining the viscosity structure near fault zones. The shear stress in front of the fault tip increase significantly within several decades after the event for models with a shallow low-viscosity zone beneath the fault. This accelerated stress accumulation is consistent with the observed phenomenon of earthquake migration along the North Anatolian fault zone.