Abstract: In order to envelop the necks of a series of continuously moving bottles with decorative or informative tubular attachments, an elongate tube of heat-shrinkable plastic material is flattened first in one longitudinal plane and then in another longitudinal plane, perpendicular to the former, to produce a sheath with two substantially flat sides bearing the traces of a first pair of creases while being bounded by a second pair of creases. The longitudinally advancing sheath is cut into clippings of predetermined length that are advanced codirectionally therewith but at higher speed along a sloping guidepath in which the existing creases are caused to converge while the original creases reappear as the two sides are progressively spread apart.