A time-stepping finite element method is used to predict the viscoelastic stresses that arise in a tube-tooling wire-coating problem. The polymer melt HDPE is modelled by a multi-mode Phan-Thien/Tanner constitutive equation. Different flow geometries are considered to address optimisation of the process with respect to minimising the stress induced within the coating produced. The influence of the die itself and the various modes are considered. Relaxation times range for a three-mode model from 10(-2) to 10(2) s and for a seven-mode model from 10(-3) to 10(3) s. Typical Weissenberg numbers may range up to 10(4). Three modes are sufficient to adequately describe the flow, and shorter/narrower draw-down regions are identified as being preferable. Once an adequate land length has been gathered, that has relaxed the flow stresses prior to draw-down, the actual details of die design are found to be inconsequential to the induced stresses in the delivered coatings. (C)2000 Elsevier Science B.V. All rights reserved.