A cutting unit includes a stationary frame, a cutting drum, and an anvil drum. The cutting drum and the anvil drum are arranged one over the other for cutting web material fed therebetween. The upper drum is centerd on a rotatable arbour and rotatably supported in the stationary frame. The lower drum is rotatable and movable towards and away from the upper drum. A rotatable carrier, movable towards and away from the upper drum, includes at least two contact rollers. The lower drum is shaftless and rests on the contact rollers. At least one contact roller is situated on either side of a central vertical plane of the lower drum for providing support of the lower drum by the contact rollers only. A pressing device moves the carrier and the lower drum towards and against the upper drum for providing cutting pressure between the upper drum and the lower drum.

A method of cutting a continuous hollow tubular member having a fully expanded configuration with an outer diameter D, includes the steps of feeding the continuous hollow tubular member in the fully expanded configuration to a cutting station, cutting the continuous hollow tubular member into a plurality of hollow tubular members, each of which has a first flattened end and expanding the first flattened end of the plurality of hollow tubular members to the fully expanded configuration such that the first end of the plurality of hollow tubular members has an outer diameter D.