A hydrodynamic model of the slip zone between the descending oceanic crust and the overriding continents is used to explain the observed constancy of the dip angle for most island arc--trench systems. By allowing the thickness of the slip zone to vary with depth, the descending plate is acted upon by a nonhydrostatic pressure force and a viscous shear force of a hydrodynamic origin which can balance the gravitational force acting on the plate. In this way the plate adheres to the overriding continent, maintaining an angle of descent dictated by the geometry of the overriding continent. An estimate of the slip zone thickness at the earth's surface is derived that is consistent with observations. Estimates of the slip zone viscosity, shear stress, and dissipation are also obtained that are in agreement with accepted values.