A generally tube-shaped package that has a tear strip joined to a web of packaging film, the tear strip incorporating an encapsulated tear notch. The package is filled with cookie or bread dough. In accordance with one embodiment, the tear strip is part of a tape that is joined to a web of packaging film. Preferably, the tear strip has a tear bead. Optionally, tearing off of the tear strip provides access to a peel seal, which in turn must be sundered to gain access to the dough. In accordance with another embodiment, the tear strip comprises a portion of a web of packaging film, which portion is bounded by a pair of mutually parallel capped tear lines. A tear bead is disposed between the tear lines. Methods of manufacturing such packages are disclosed.