Corner flows of Newtonian and non-Newtonian fluids are used to model the flow in a subduction zone which is viscously driven by the motions of the converging plates and the descending slab. The pressures induced by the flow tend to lift the slab up beneath the overriding plate thereby offsetting the tendency of gravity to align the slab with the vertical. The low angles of subduction observed in Peru and Central Chile may be the result of strong dynamic pressures forcing the slab up against the overriding plate. Viscous coupling between the overriding plate and the downgoing slab is essential if the nonvertical dips of slabs are a consequence of the balance between gravitational and pressure torques. For a Newtonian mantle, shear stresses and pressures on the top of the slab are comparable. If the mantle is non-Newtonian, however, the pressures greatly exceed the shear stresses, for most acute dip angles. Thus frictional forces on the top and bottom surfaces of slabs are less important in resisting slab decent into a non-Newtonian mantle than they are in resisting penetration into a Newtonian mantle.