The invention relates to a device for the flow-through treatment of web-shaped, gas-permeable material, in particular for drying woven or non-woven fabrics, having the following characteristics: a sieving drum (5), which is rotatably supported and which is connected to a vacuum generator and which has a permeable outer circumference, wherein the material web (M) to be treated rotates around part of the outer circumference of the sieving drum (5); a treatment chamber (BH), which accommodates the sieving drum and to which the gas to be treated, preferably heated air, is supplied; inside the treatment chamber (BH), a sieving cover (SD) or corresponding flow-conducting elements, which surround the sieving drum (5) in the area around which the material web (M) is wound and by means of which the gas flowing into the treatment chamber (BH) is conducted in the direction of the sieving drum surface. According to the invention, the wall (W) of the treatment chamber (BH) facing the outer circumference of the sieving drum (S) in the area around which the material web (M) is wound has a decreasing distance (a1, a2, a3) from the surface of the sieving drum (S) in said area.