An apparatus for mirror-polishing a thin plate, wherein uniformity of tightness in a stretched condition across an elastic film can be achieved and a polishing pressure distribution on the thin plate is uniformalized, so that constant polishing stock removal is realized and high flatness polishing is made possible. In the apparatus, the thin plate is held on a thin plate support mounted on a rotatable press member and the thin plate is pressed to a polishing means by the press member, and the apparatus has features that a holding surface for the thin plate is formed by a flexible elastic film; the elastic film is fastened to the press member or a part mounted thereto in a condition that the elastic film is sandwiched between a spacer and a holding piece; and a pressure, which presses the thin plate held on the elastic film to the polishing means, is adjusted by applying a back pressure to the thin plate with a fluid feed means, while adjusting tightness of the elastic film by the space.