Recent high-resolution seismic experiments reveal that the crust beneath the San Gabriel Mountains portion of the Transverse Ranges thickens by 10–15 km (contrary to earlier studies). Associated with the Transverse Ranges, there is an anomalous ridge of seismically fast upper mantle material extending at least 200 km into the mantle. This high-velocity anomaly has previously been interpreted as a lithospheric downwelling. Both lithospheric downwelling and crustal thickening are associated with the oblique convergence of Pacific and North America plates across the San Andreas Fault, though it seems likely that the lithospheric downwelling is driven at least partly by gravitational instability of the cold lithospheric mantle. We show by means of numerical experiment that the balance between buoyancy forces that drive deformation and viscous stresses that resist deformation determines the geometry of crustal thickening and mantle downwelling. We use a simple two-layered lithospheric model in which dense lithospheric mantle overlies relatively inviscid and less dense asthenosphere and is overlain by buoyant crust. External plate motion drives convergence, which is constrained by boundary conditions to occur within a central convergent zone of specified width. A fundamental transition in the geometry of downwelling is revealed by our experiments. For slow convergence, or low crustal viscosity, downwelling occurs as multiple sheets on the margins of the convergent zone. For fast convergence or crust that is stronger than mantle lithosphere a single downwelling occurs beneath the center of the convergent zone. This complexity in the evolution of the system is attributed to the interaction of crustal buoyancy with the evolving gravitational instability. In order for a narrow downwelling slab to have formed beneath the Transverse Ranges within the last 5 Myr, the effective lithospheric viscosity of the convergent region is at most about 1020 Pa s.