PURPOSE: To simplify a wrapping machine for cigarette packs or the like by supplying web to a suction drum with a speed faster than the controlled, severing with cutter device mounted on the suction drum, and taking out straight in the drum tangent direction.

CONSTITUTION: Feed rolls 4, 6 rotate with peripheral speed controlled slower than a suction drum 8 and send out a wrapper web 2 to the suction drum 8. A cutter blade 10 attaches to the suction drum 8, turns along with the drum 8 and severs leader portion of the web 2 sucked by the drum 8 in cooperation with a fixed blade 12. Leader portion of the severed web 2 is carried in the tangent direction of drum 8 at the same speed thereof by a delivery conveyor 14, and supplied to the gap between eccentric pinch rollers 15, 17 that have cam projections 15A, 17A, where the web 2 is completely severed. Then a wrapping portion 2A of the severed web 2 is delivered to a conveyor 24 and supplied by crossing the path of articles 30 to wrap them.