PURPOSE: To provide a method and an apparatus for continuously cutting a material in sliver or strand form, especially an artificial fiber tow.

CONSTITUTION: This apparatus comprises a cutting wheel 1 provided with a multiplicity of cutting knives 3, a pressure roller 4 for producing on a wound material in silver or strand form a cutting pressure acting on the cutting knives 3, an opening and closing device 5 by means of which the pressure roller 4 can be moved, an adjusting member 6 by which a preset distance can be adjusted between the pressure roller 4 and the cutting knife 3, a damping means 1 by which the contact pressure exerted by the pressure roller 4 on the material on the knife 3 is adjusted to a fixed pressure, and a distance measuring device 8 by which the distance between the pressure roller 4 and the cutting knife 3 is monitored. In the cutting method, the cutting force is excellently constant, the life of use of the cutting knives is long and the qualities of the cut material are uniform.