A drum cutting machine has a rotary drum and has a plurality of blades arranged along the contour of the rotary drum. The lateral surface of the rotary drum is provided with a multiplicity of holes. A supporting part matches the contour of the rotary drum and has for each of the blades a bearing point that defines the position of the cutting edge. A blade box for such a machine makes it easier to move the blades into the correct position, thereby reducing the complexity in terms of maintenance.