Abstract: A multiple chucking device is disclosed, which is suitable in particular for clamping in grooves of a machine table. The device includes a clamping block, at least one clamping piece, and an end block which are mounted on a pair of guide axles. The clamping block is rigidly supported on the pair of guide axles, and the clamping pieces and the end piece are adjustable in a longitudinally displaceable manner, and may be secured by locking screws that engage the axles. The clamping piece and the end block are equipped with a clamping jaw in the form of a wedge collet, and with a support housing a recess, in which an obliquely downwardly extending tightening screw is located. The screw is tightened by the wedge collet so as to engage and clamp a workpiece.