[1] Oblique convergence across the San Andreas Fault in southern California has lead to rapid uplift of the San Gabriel Mountains since 5 Ma. Tomographic models of this region include a sheet-like, high velocity anomaly, extending to depths > 200 km. One proposed mechanism for the formation of this feature is gravitational instability of the lithosphere, resulting in a cold thermal downwelling. We present a systematic study of the sensitivity of lithospheric deformation ( lithospheric downwelling, topography, deflection of the Moho, convergent velocity profile) to the viscosity structure in 2-D numerical models of lithospheric instability, including a pre-existing zone of weakness. Strike-parallel strain within a convergent region should create a local zone of weakness due to the non-Newtonian response of the lithosphere. Such a weak zone can focus convergent motion, increasing and localizing the growth-rate of a lithospheric instability. We find that the observed characteristics of deformation depend on the width (x(w)) and relative viscous weakening factor (f(w)), the ratio of crust to mantle-lithospheric viscosity (eta(c)/eta(m)), and the absolute viscosity of the lithosphere ( h m). For the San Gabriel Mountains, we find that a range of models is capable of reproducing the observed Moho deflection and depth extent of the downwelling within the short time since the onset of convergence. However, only a small subset of models, (x(w) = 20 km, f(w) = 50 - 100, eta(m) = 7.5 x 10(20) - 1.5 x 10(21) Pa s, eta(c)/eta(m) > 100) reproduce both the narrow, high topography and horizontal shortening profile.