The invention relates to a press (1) for producing a tampon (8) by radially pressing an absorbent material by means of compression jaws (2, 2′, 3) which have respective penetrating segments (4, 5) for embossing grooves (9, 10) into the absorbent material, one compression jaw (3) the penetrating segment (5) of which is designed as a strip having flat lateral faces projecting into the compression space and one compression jaw (2, 2′) the penetrating segment (4, 4′) of which is designed as a rib having undulated lateral faces projecting into the compression space being alternately arranged. A projection of the strip onto a peripheral surface of the tampon (8) present in the compression space represents a straight line and a projection of the undulated rib onto the peripheral surface represents an undulated line.