Recent interpretations of Himalayan-Tibetan tectonics have proposed that channel flow in the middle to lower crust can explain outward growth of the Tibetan plateau, and that ductile extrusion of high-grade metamorphic rocks between coeval normal- and thrust-sense shear zones can explain exhumation of the Greater Himalayan sequence. Here we use coupled thermal-mechanical numerical models to show that these two processes-channel flow and ductile extrusion-may be dynamically linked through the effects of surface denudation focused at the edge of a plateau that is underlain by low-viscosity material. Our models provide an internally self-consistent explanation for many observed features of the Himalayan-Tibetan system.