Meaurements of strain accumulation adjacent to the San Andreas fault indicate that the zone of strain accumulation extends only a few tens of kilometers away from the fault. Such a narrow zone of cyclic strain accumulation and release is consistent with the measured coseismic strain and inferred stress drop during the 1906 earthquake. The restricted zone of cyclic accumulation and release of elastic energy adjacent to major strike-slip faults has been attributed to the damping effect of a viscoelastic asthenosphere. However, to explain the narrowness of the zone on the San Andreas fault, it is necessary to conclude that the thickness of the lithosphere is 10--20 km. This does not appear to be consistent with the relatively low surface heat flow measurements. In this paper an alternative four layer model is proposed to explain the behavior of the San Andreas fault. An upper elastic plate extends to a depth of about 15 km, the depth of the deepest seismicity on and adjacent to the fault. Beneath this upper elastic plate is a soft, intracrustal asthenosphere that exhibits a viscoelastic behavior. The viscous behavior of these crustal rocks at relatively low temperature is attributed to either the presence of quartz, which is known to have a very softj rheology, or the presence of water that can lead to pressure solution creep or to both effects. Beneath this soft layer is a second elastic layer made up of the tough lower crustal and upper mantle rocks. And beneath this second elastic layer is the asthenosphere. There is extensive geological and geophysical evidence for the existence of an intracrustal asthenosphere both in California and elsewhere. We show that the damping due to the intracrustal asthenosphere can explain the observed narrow zone of cyclic strain accumulation and release on the San Andreas fault.