Absorbent pants with a longitudinal direction and a transverse direction at right angles to the longitudinal direction and having an absorption core arranged between a liquid-tight cover sheet and a liquid-permeable cover sheet. The diaper pants have a front portion, a rear portion and an intermediate crotch portion, and a front edge and a rear edge extending substantially in the transverse direction and forming a waist opening, two side edges extending substantially in the longitudinal direction and forming two leg openings. An elastic sheet material is arranged at least along the waist opening of the diaper pants and extends at least from the waist opening to the leg openings, the elastic sheet material being secured to the absorption core in a substantially unstretched state.