A cigarette packing machine for producing a rigid packet a hinged lid has a first packing unit which folds a first blank about a group of cigarettes to form an outer container with a hinged lid; and a second packing unit which folds a second blank about the outer container to form a tubular slide surrounding the outer container to slide axially with respect to the outer container; the tubular slide has a transmission member, in turn having a first end integral with the lid, a second end opposite the first end and integral with the slide, and a deformable intermediate portion having a U-shaped fold between the outer container and the slide.