We use boundary element methods to develop antiplane, strike-slip earthquake cycle models consisting of faulting in an elastic plate with possibly different thickness and stiffness on either side of the fault overlying a linear, Maxwell viscoelastic substrate. We show that isolated plate models that neglect the coupling of the plate to the underlying substrate might significantly overpredict the asymmetry in deformation across the fault. We also show that flow in a low-viscosity channel in the lower crust could significantly contribute to the asymmetry. Through a fully probabilistic scheme, we invert geodetic data across three strike-slip fault systems for effective elastic thickness and elastic stiffness on both sides of the fault using geological and geophysical constraints. For the Renun segment of the Great Sumatra fault, inversion results show the elastic layer on the east side is stiffer than the west side but the effective elastic thicknesses are not resolvable. For the Carrizo segment of the San Andreas fault, the inversion results slightly favor a thicker elastic layer on the east side (∼2.2 times) but stiffer layer on west side (∼1.2 times); however, uniform effective elastic thickness and stiffness cannot be ruled out. For the Aksay segment of the Altyn Tagh fault in northern Tibet, inversion results show the effective elastic crust of the Tarim Basin must be stiffer and thicker than the effective elastic crust of the Tibetan Plateau to the south, but the viscosity of a hypothesized mid-crustal Tibetan channel is not resolvable.