The present disclosure relates to a cross-flow shredder for grinding material with integrated dust-tight conveying means and air recirculation, and a method for grinding material using the cross-flow shredder according to the disclosure. An apparatus and a method for comminuting material to be ground are disclosed, the apparatus comprising a feed opening for material to be ground, a feed device, a cross-flow shredder, two screw conveyors for conveying the material to be ground and an intermediate dust-tight bunker, the two screw conveyors being connected in a dust-tight manner to the cross-flow shredder on the respective feed side and in a rod-tight manner to the intermediate bunker on the discharge side, the intermediate bunker being connected to the cross-flow shredder via a hose or pipe system, and the intermediate bunker having a discharge opening closed by a slide valve.