The invention relates to a device for tightening a tubular casing filled with a product by means of several pairs of displacers, wherein the mutually overlapping displacers of each pair encompass an opening, both displacers adjoining to the encompassed opening in two overlapping points per pair. The displacers are configured for a linear tightening movement depending on the varying size of the openings, the openings being located one behind the other in the axial direction of the tubular casing encompassing a passage. The openings are not congruent with the passage, the overlapping points being at a distance from the passage during the predominant part of the tightening movement. The invention allows the subdivision of the filled tubular casing into packaging units, thereby preventing or reducing the risk of damages to the tubular casing.