Abstract: An apparatus for perforating sheet material during travel of the latter in a given plane. The apparatus includes rotary punches which penetrate through the sheet material during travel thereof. The punches turn around an axis extending transversely with respect to the direction of travel of the sheet material so that each punch approaches the plane of the sheet material to initially contact the latter and then penetrate through and be retracted from the sheet material. Each punch has a concave punching end surface forming part of a cylinder whose axis is perpendicular to the punch axis and parallel to the axis around which each punch turns while approaching the plane of the sheet material. Thus, each punch has at its punching end leading and trailing tips which lead and trail considered in the direction of rotation of each punch.