A polymeric fiber postspinning draw model is developed. The fiber is stretched between the take-up roll and the draw roll and then relaxed between the draw roll and the relax roll. The behavior of the polymeric material is described by a cooperative elastic-viscoplastic model for a wide range of temperatures and strain rates. The profiles of the fiber velocity, stress, strain rate, and temperature between the different rolls are simulated via the coupling of the cooperative model with the mass, momentum, and energy equations and the boundary conditions. Simulations are conducted with the finite-element method. The computed results show an increase in the fiber stress between the take-Lip roll and the draw roll due to the molecular orientation and the increase in the crystallization percentage. The sliding distance of the fiber on the draw roll is related to the draw ratio and fiber stiffness. A dramatic drop in the fiber strain rate on the draw roll leads to relaxation of the intermolecular resistance followed by a freeze of the fiber structure when the strain rate vanishes to zero on the draw roll and between the draw roll and the relax roll. (c) 2006 Wiley Periodicals, Inc.