A cigarette making machine for making cigarettes containing a core of material different from that of a surrounding annulus of tobacco comprises a conveyor, a conveyor band for forming a continuous substantially flat initial layer of tobacco on the conveyor, a further conveyor band for feeding a core onto the initial layer of tobacco, side walls for at least partially confining the sides of the core along a predetermined distance after the core has been fed onto the initial layer of tobacco, and a shower for feeding tobacco onto side portions of the initial layer, on opposite sides of the core, while the core is being confined by the side walls.