SUMMARYAnnular pressure-tooling extrusion is simulated for a low density polymer melt using a Taylor-PetrovGalerkin ÿnite element scheme. This represents industrial-scale wire-coating. Viscoelastic uids are modeled via three forms of Phan-Thien=Tanner (PTT) constitutive laws employed for short-die and full speciÿcation pressure-tooling. E ects of variation in Weissenberg number (We) and polymeric viscosity are investigated. Particular attention is paid to mesh reÿnement to predict accurate results. The impact of variation in shear-thinning and strain-softening properties is considered upon the modelling predictions. For the short-die ow, the in uence of the lack of strain softening is identiÿed. For the full-die ow and more severe deformation rates, the linear PTT model failed to converge. In contrast, the exponential PTT model is found to be more stable numerically and to adequately re ect the material response. Comparing short-die and full-die pressure-tooling results, shear rates increase 10-fold, while strain rates increase one hundred times.