Geodetic studies have shown that deformation rates around several major strike‐slip faults are asymmetric. This asymmetry is often explained in terms of a crustal‐scale contrast in elastic properties across the fault. Motivated by the fact that elasticity variations for different rock types under similar ambient conditions are generally modest, whereas effective viscosity may vary over orders of magnitude, we have developed earthquake‐cycle models to evaluate whether contrasts in viscosity structure and effective plate thickness can explain observed asymmetric surface deformation. We find that an increased plate‐thickness contrast results in a more asymmetric surface‐velocity profile. Furthermore, for the same plate‐thickness contrast, asymmetry of the surface deformation is most pronounced in models with a low‐viscosity substrate. Initially, velocities relative to a point on the fault are higher on the side with the thin plate; however, late in the interseismic interval this reverses, and these velocities are higher on the side with the thick plate. Models with a contrast in the substrate viscosity on either side of the fault and a uniform plate thickness show behavior similar to that of the variable‐thickness plate models. In both suites of asymmetric models, the surface velocity at the fault varies through the earthquake cycle. This is necessary to reconcile symmetric coseismic deformation, asymmetric interseismic deformation, and the requirement of zero strain in the blocks on either side of the fault over an earthquake cycle. Given the modest asymmetry in surface deformation for models capable of producing localized interseismic deformation around the fault (i.e., models with high substrate viscosities), we conclude that lateral contrasts in viscosity or effective plate thickness cannot produce dramatic asymmetries in Global Positioning System surface‐velocity profiles across major strike‐slip faults.