Abstract: A chuck means for flat workpieces, in particular semi-conductor wafer for the chemical-mechanical polishing, comprising a circular housing which is attached to a driving spindle for rotation therewith and has a top wall and an annular side wall, a retaining ring which forms the lower part of the side wall, a chuck plate of rigid, however elastically deformable material which has an upper and a lower side and a plurality of openings at the lower side as well which openings are in connection with radial and axial parallel passages in the chuck plate, the passages being in fluid connection with an axial passage in the spindle, the axial passage being connected to a vacuum and/or fluid source, the chuck plate being floatingly and vertically movably located in the housing, a plurality of pressure chambers above the chuck plate, the pressure chambers having lower wall portions which are yieldable and engage the upper side of the chuck plate, pressure manifold means which are connected with a fluid source under pres