The invention relates to a method for cutting webs of material (12), which rest upon the peripheral surface of the cutting and feed roller (1) and to a cutting and feed roller (1). These webs of material are cut through by means of a cutting device that, when in its position of rest, is essentially located inside the lateral surface (2) of the cutting and feed roller (1). This cutting device comprises at least one blade (4) that, when cutting the web of material (12), passes through an opening (3) located inside the lateral surface (2) of the cutting and feed roller (1). The opening located inside the lateral surface (2) of the cutting and feed roller (1), through which the at least one blade (4) passes during the cutting process, is closed when a cutting process is not occurring.