Although Mars is currently not tectonically active, it may have experienced plate tectonics early in its history. The southern hemisphere of Mars possesses a thick crust which probably renders the lithosphere positively buoyant. In this paper we present numerical and scaling arguments which show that if the area of positively buoyant lithosphere grows beyond a critical fraction (≈50% for Mars), plate tectonics will stop. Heat transfer through the buoyant lithosphere is inefficient, which causes mean mantle temperatures to increase as the surface area of buoyant lithosphere increases. The resulting reduction in mantle viscosity reduces shear stresses; if these shear stresses drop below the yield strength of the lithosphere, plate motions will cease and the planet will behave as a one-plate system. Thus the end of plate tectonics on Mars is a natural consequence of the growth of the southern highlands. Similar arguments for the Earth predict that it should operate in the plate tectonic regime now but that it may have experienced stagnant lid convection in the past.