A machine for filling containers, comprising: a conveying device; a plurality of handling units configured to be moved by the conveying device along a path, each of the plurality of handling units having: a support device configured to receive and retain a corresponding container; and a filling device configured to feed a pourable product into the container; and at least one actuator associated with the plurality of handling units and configured to rotate each support device about a corresponding first rotation axis, the at least one actuator including a single motor and a transmission to connect the single motor with at least two support devices.