Abstract: A machine to insert and stake rivets in a flexible sheet is disclosed. The machine includes a riveting punch and an associated anvil and, in cooperation therewith a clamping device having parts which float relative to the riveting punch and the anvil so that during insertion and staking of the rivet, the sheet, and more particularly the opening in the sheet for receiving the rivet can be adequately supported at a variety of distances relative to the midpoint between the riveting punch and anvil. The clamping device includes a frame carried by the punch and a sleeve carried by the anvil which cooperate to clamp the flexible sheet; and the frame and sleeve are resiliently associated with the punch and the anvil such that portions of the riveting motion of the press will cause clamping prior to riveting.