Abstract: A machine is of the type comprising an oscillating movable head with a tool-holding spindle, driven in rotation above a lens-support. The lens-support is borne by a vertically movable spindle which is mounted inside a sleeve, flared out at its upper part to form two bearing surfaces and, the lens-support comprises a ledge which surrounds the part of the sleeve containing the bearing surfaces. The lens-support rests on a head mounted for free rotation in a fixed pivot so that when the spindle is moved upwardly, the lens-support is immobilized in a horizontal position, to deposit the lenses to be polished thereon, or to remove them after the polishing operation. When the spindle is moved downwardly, the lens-support, then at a distance from the bearing surfaces, can oscillate freely during the lens-polishing operation, under the effect of the movable oscillating head.