For the production of cigarette packs (10) with shrink-treated outer film, the packs (10) are subjected in a continuously rotating shrinking revolver (19) to a heat treatment effecting the shrinkage. To each pack (10) there are assigned, in the region of the shrinking revolver (19), heating plates (22, 23), which bear against the front side and rear side of the pack (10) or of the film.