Fault plane of a strike-slip fault is suggested to be near vertical by the Anderson Theory of Faulting. However, the San Andreas Fault (SAF), a dominant component of the transform boundary between the Pacific and the North American Plate, is found to have southwest dipping fault plane near the western Transverse Range and northeast dipping fault plane in the Southern segment of SAF. The mechanism controlling fault dip variation along SAF is not known yet. We utilize the 3D finite element thermomechanical, viscoplastic model to simulate deformation in the San Andreas Fault system. The big bend of the fault is an existing geometry in our model as an initial condition. The numerical experiments demonstrate that regional lower crust strength variation along fault striking may result in corresponding fault dip direction alteration. In transpressional background, the block with lower crust of higher viscosity outdents into the other with weak lower crust. In turn, upper crust overlying weak lower crust up thrusts over the stronger block, forming fault dip pointing to the block with weak lower crust. Evidenced by geophysical data that the Great Valley and south coast area are of stronger lower crust, the predicted fault dip direction is supposed to be SW near the Big Bend and NE in the southern segment of SAF, consistent with field observations. This self-consistent model will also shed light on the left-slip Garlock Fault, which intersects the right-slip SAF in the western Transverse Range.