Apparatus for supplying a web of wrapping material to a chamber (Ch), wherein the chamber (Ch) is arranged to contain an object which is to be wrapped into the supplied web, wherein a wrapping material inlet (In) guides into the chamber (Ch), wherein the wrapping material supplying apparatus comprises - a holding member with a front edge (FE.2) pointing towards the wrapping material inlet (In), - a conveying member with a front edge (FE.3) pointing towards the wrapping material inlet (In), and - a conveying member drive, wherein the conveying member is moveable with respect to the wrapping material inlet (In) between - at least one remote position and - an injecting position, wherein the drive is arranged to move the conveying member - from the or one remote position - in a conveying direction - into the injecting position, and wherein the wrapping material supplying apparatus is arranged - to keep a web of wrapping material in a position between the holding member and the conveying member such that a segment (Sg) of the web protrudes beyond at least one front edge (FE.2, FE.3) towards the wrapping material inlet (In) at least if the conveying member is in the injecting position, - to move the kept web in the conveying direction towards the wrapping material inlet (In), and - to inject the moved and protruding web through the wrapping material inlet (In) into the chamber (Ch), characterized in that the wrapping material supplying apparatus further comprises at least one pressing element (4.1,4.2,...) which - is mounted at the front edge (FE.3) of the conveying member and - comprises a front edge (FE.4.1, FE.4.2,...) pointing towards the wrapping material inlet (In), wherein at least one notch (5.1, 5.2,...) - is cut into the front edge (FE.2) of the holding member and - is positioned adjacent to the or one pressing element (4.1, 4.2,...), wherein - the respective maximal width (W.4.1, W.4.2,...) of the or every pressing element (4.1,4.2,...) is smaller than the respective minimal width (W.5.1, W.5.2,...) of the or one notch (5.1, 5.2,...) positioned adjacent to this pressing element (4.1, 4.2,...) and - the respective maximal width (W.5.1, W.5.2,...) of the or every notch (5.1, 5.2,...) is smaller than the width (W.2) of the front edge (FE.2) of the holding member, wherein the width is the largest dimension in a direction perpendicular to the conveying direction, and wherein the or at least one pressing element (4.1,4.2,...) engages into the notch (5.1, 5.2,...) positioned adjacent to this pressing element (4.1, 4.2,...) at least when the conveying member is in the injecting position, thereby - pressing the protruding segment (Sg) of a web being kept between the holding member and the conveying member through the adjacent notch (5.1, 5.2,...) and - clamping the protruding segment (Sg) of the web at least between the holding member and the or at least one pressing element (4.1, 4.2,...). - a holding member with a front edge (FE.2) pointing towards the wrapping material inlet (In), - a conveying member with a front edge (FE.3) pointing towards the wrapping material inlet (In), and - a conveying member drive, - at least one remote position and - an injecting position, - from the or one remote position - in a conveying direction - into the injecting position, and - to keep a web of wrapping material in a position between the holding member and the conveying member such that a segment (Sg) of the web protrudes beyond at least one front edge (FE.2, FE.3) towards the wrapping material inlet (In) at least if the conveying member is in the injecting position, - to move the kept web in the conveying direction towards the wrapping material inlet (In), and - to inject the moved and protruding web through the wrapping material inlet (In) into the chamber (Ch), - is mounted at the front edge (FE.3) of the conveying member and - comprises a front edge (FE.4.1, FE.4.2,...) pointing towards the wrapping material inlet (In), - is cut into the front edge (FE.2) of the holding member and - is positioned adjacent to the or one pressing element (4.1, 4.2,...), - the respective maximal width (W.4.1, W.4.2,...) of the or every pressing element (4.1,4.2,...) is smaller than the respective minimal width (W.5.1, W.5.2,...) of the or one notch (5.1, 5.2,...) positioned adjacent to this pressing element (4.1, 4.2,...) and - the respective maximal width (W.5.1, W.5.2,...) of the or every notch (5.1, 5.2,...) is smaller than the width (W.2) of the front edge (FE.2) of the holding member, - pressing the protruding segment (Sg) of a web being kept between the holding member and the conveying member through the adjacent notch (5.1, 5.2,...) and - clamping the protruding segment (Sg) of the web at least between the holding member and the or at least one pressing element (4.1, 4.2,...).