A gas swept tube mill has a rotary shell (1) supported on a bearing (5) by a slide ring (3), which is reinforced by a stiffening web plate (4). Ground material and gas pass out of the mill shell through a sieve plate (10) and openings (8) in a frustoconical connecting section (12) into a stationary casing (9). The wider end of the section (12) is of similar diameter to the shell (1), to which it is fastened, and the narrower end of the section (12) is fastened to a drive shaft (7) for rotating the shell (1).