Shredded tobacco is supplied from a storage reservoir to one or more cigarette making machines by way of discrete pneumatic conveying pipes. The reservoir receives fresh tobacco at regular or irregular intervals so that the quantity of tobacco in its interior is constant. The contents of the reservoir are maintained in suspension so that at least the major part of the supply of tobacco shreds forms a fluidized bed which is located directly below the intakes of the conveying pipes. When a machine requires a batch of tobacco shreds, the respective pipe is connected to a suction generating device so that it draws air from the region between the underside of the fluidized bed and the upper side of the bottom wall of the reservoir whereby the ascending current of air entrains tobacco particles directly from the fluidized bed. The supply of tobacco in the reservoir can be converted into a fluidized bed by mechanically agitating the reservoir so that the shreds move up and down and/or by causing a plurality of streamlets of compressed air to rise through perforations in the bottom wall of the reservoir. The latter may have a circular, semicircular or polygonal cross-sectional outline.