In this paper, we use two new models and the irreversible KBKZ model of Wagner (Rheol Acta 18:681-692, 1979) to describe the famous experiments of Meissner (Rheol Acta 10:230-242, 1971) on the recoil of polyethylene. The new models are based both on network and reptation-type ideas. One of the new models (PTT-X) is a member of the PTT family and shows good agreement with polyethylene data in shearing, elongation, and recoil from elongation.