A machine to manufacture cartridges for electronic cigarettes comprising a casing made of plastic material; the manufacturing machine comprises a drum rotating at a predetermined pitch around its own vertical rotation axis, which receives an orderly mass of empty casings from a feeding conveyor, in correspondence to a collecting station, and feeds them through a succession of processing stations; in which, the first drum is provided with a plurality of peripheral seats, each designed to receive a respective casing and which are divided into groups comprising the same number of seats arranged substantially in line so as to form, in plan view, a polygon on the surface of the first drum; in which the casings of the seats of a same group are simultaneously subjected to the processes in correspondence to the succession of processing stations.