An apparatus for cutting ocular lens materials is disclosed which includes a rotating drive unit, a chuck for holding the lens material, a main shaft for transmitting a rotational force from the rotating drive unit to the chuck, and a coupling for supporting the main shaft and the chuck in a freely rotatable way; the chuck comprising finger members that are normally urged toward the side where they are closed and a cylinder portion for operation in such a way as to open the finger members; the chuck and the main shaft being connected concentrically; a passageway being provided for applying a working pressure from outside to the cylinder portion.