An apparatus for feeding a wrapping web to a wrapping station, where a product is to be wrapped with the wrapping web, includes a backstand for holding a supply roll of the wrapping web and for unwinding and rewinding the wrapping web. The wrapping web falls under gravity on a conveyor which transports the wrapping web to the wrapping station without using bend rollers. The unwinding or rewinding speed of the backstand is controllably adjustable. An unused length of the wrapping web after wrapping is rewound onto the supply roll, leaving a portion dangling loosely from the supply roll and above the conveyor. Thus, the wrapping web can be automatically fed on demand to the wrapping station without human intervention and without the need of pre-feeding the wrapping web into the wrapping station.