The packaging machine includes a wrapping tunnel, adapted to form a tube of plastic film around a group of articles and a feed conveyor, adapted to feed articles to be packaged toward the wrapping tunnel. An elevator is positioned between the feed conveyor and the wrapping tunnel, and is movable vertically from a lower position, to receive articles coming from the feed conveyor, to a higher height, to transfer articles to the wrapping tunnel. A pusher is arranged to push articles to be packaged from the elevator into the wrapping tunnel. An auxiliary conveyor is also provided between the feed conveyor and the elevator. An upender is associated with the auxiliary conveyor, adapted to be arranged selectively in an active position, to co-act with the auxiliary conveyor to upend articles coming from the feed conveyor and transfer them toward the elevator, and in a deactivated position.