Abstract: Device for cutting band-shaped or strand-shaped material, having a cutting device in the form of a cutter roller, in which outwardly-pointing cutting edges which are arranged at a uniform distance from one another connect two circular disc-shaped or annular bodies to one another, which bodies hold the cutting edges, and the material to be cut via these cutting edges forms a lap superimposed in several coil layers, the radial innermost position of which lap is cut by the pressure which acts in intensified manner as a result of a loading body. The cutter blades, the cutting edges of which cut the material, are arranged for reducing the bending stress in such a way that they are at a setting angle alpha of 5.degree. to 25.degree. to the radial direction of the device, with the cutting edges pointing in the direction of movement of the cutter roller.