A machine for filling containers, including a plurality of filling spouts, and a cleaning device comprising a plurality of individual tubular collecting elements rigidly mounted on a collection tube, and a device for moving the collection tube between a retracted position and a service position in which the collecting elements are in contact, via the upstream ends thereof, with the filling spouts. The collection tube laterally supports the collecting elements, such that, in the retracted position, the collecting elements are arranged between the filling spouts. The moving device capable of moving the collection tube from the retracted position thereof to the service position thereof by at least one downward vertical translational movement, followed by a horizontal movement.