Abstract: The disclosure relates to a machine for making a plastic covering on a rigid base article which in the illustrated form comprises a glass bottle and a conforming shrunken plastic covering thereon. The plastic is fed in oriented sheet form to the turret apparatus, cut into lengths and wrapped and seamed on successive mandrels as sleeves. Bottles are simultaneously processed to preheat condition and indexed over the sleeves, the latter telescopically assembled on the rigid base article, i.e., the bottle, and the combination carried to a heat tunnel. The plastic sleeve shrinks into snug surface fit on the adjacent surface portion of the rigid base article.The bottle is preheated in one of two embodiments by: (1) a preheat tunnel on the machine which raises the bottles from room temperature to about 220.degree. F., or (2) the preheat is carried over as latent heat in the glass bottle from the annealing lehr, a part of the bottle manufacturing process.