Vacuum hold-down apparatus is used for holding sheet material in place while it is being worked on by a tool. The apparatus comprises a means defining a generally horizontally disposed upwardly facing sheet material supporting surface. The supporting surface means includes a bed having a gas impermeable base portion and a gas permeable body portion disposed on the base portion. Means are provided for connecting a vacuum source to the gas permeable body portion of the bed to effect a vacuum within the body portion. A bed penetrable by a tool and a support means for the bed is disclosed as a combination in an apparatus for working on sheet material. The penetrable bed includes a gas impermeable base portion and a gas permeable body portion disposed on the base portion. A vacuum source is connected to the gas permeable body portion of the bed to hold the sheet material against a sheet material supporting surface while the sheet material is being worked on by the tool. Various specific embodiments of the vacuum hold-down apparatus are disclosed.