Abstract: The invention provides a vacuum chuck for retaining a planar workpiece. The chuck comprises a support member (1) providing a planar surface (2) for supporting a workpiece (3). Passages (4a, 4b), extend through the support member (1) from said planar surface (2) thereof, said passages each being connected to a source of vacuum at a particular pressure. Valves (5, 5a), are provided for closing each said passage (4a, 4b), when the passage is subjected to both atomspheric pressure and said vacuum pressure simultaneously, said valves (5, 5a) remaining open when subjected to either atmospheric pressure or said vacuum pressure alone. By this arrangement the workpiece (3) can be cut or apertured without interfering with the vacuum pressure acting on the workpiece (3).