We have measured the surface stress on single crystal Cu(100) surfaces as induced by bombardment of the surface with the noble gas ions Ar, Ne and He at room temperature. Regardless of the ion type and energy, the induced stress is compressive and saturates as a function of sputter time at a value between 2 and 15 N/m. Saturation time and magnitude of the induced stress depend on the ion species and their energy. The time dependence can be accounted for by assuming a steady state thickness of a defective surface layer, which arises from a balance between sputtering and ion implantation.