A tearing device to be applied to a complete package (1, 2) is disclosed, consisting of an adhesive label having a base layer (3) provided with an adhesive portion and a terminal portion (32, 33, 34, 32′, 33′) acting as gripping edge for imparting a manual traction, the label being so arranged as to determine at least two points of localised application of the stress, or a point of application of the stress and a point of reaction to the stress, very close to each other, upon applying a traction on said terminal portion. A weakening line or a preferred-rupture line (4, 4′) may be provided, with the base layer being made of a material having an ultimate tensile strength higher than that of the wrapping sheath and a much lower tensile elongation than that of the wrapping sheath.