In a machine for wrapping sticks of chewing gum, sticks of substantially rectangular outline and relatively small thickness advance singly and in succession on a conveyor, arranged flat and spaced apart at a predetermined first pitch, toward a position where they are transferred to a spacing roller revolving tangentially to the conveyor and presenting peripheral seats spaced apart at a pitch greater than the first pitch; the sticks are taken up at the transfer position by a pick-up and transfer mechanism operating between the conveyor and the seats of the spacing roller, describing a trajectory that includes a movement perpendicular to the plane occupied by the sticks and producing a minimal displacement equating approximately to the thickness of a single stick.