Two modeling studies of the stress accumulation and release cycle on two-dimensional strike-slip faults have been carried out to understand better the behavior of the San Andreas fault. The first study concerns the interaction between an elastic lithosphere and an elasticoviscous asthenosphere. An analytic solution has been obtained for the stress and displacement fields due to an infinite sequence of step displacements on a two-dimensional fault. For reasonable values of the asthenospheric viscosity the periodic fault displacement is damped out several lithospheric plate thicknesses from the fault. For relatively high viscosities the strain accumulation phase between earthquakes is nearly constant; for relatively low viscosities the strain accumulation decreases with time. In a second study a series of finite element calculations have been carried out to study a depth-dependent rheology on the fault. A yield stress which decreases with depth is prescribed. It is found that the depth of the locked section of the fault decreases as stress on the fault increases. As a result, the rate of shear strain near the fault increases prior to a great earthquake.