The invention refers to a wrapping material supplying apparatus and device which supplies a web (21) of wrapping material to a chamber (Ch) which contains an object (B) to be wrapped. The web (21) is clamped between a conveying member (3) and a holding member (2) and is moved towards a wrapping material inlet (In). A pressing element (4.4) is mounted at the front edge (FE.3) of the conveying member (3) and engages into a notch (5.4) which is cut into the front edge of the holding member (2). The pressing element (4.4) presses the web (21) through the notch (5.4).