Solid-phase processing is an established technique that produces highly oriented polymer products with enhanced mechanical properties. Here we study the solid-phase die-drawing process, where a semi-crystalline polymer is pulled through a die, or over a mandrel, at an elevated temperature. After processing, the induced molecular orientation is "locked in". Finite Element simulations of the drawing process were performed in Abaqus/Explicit, using the "Arbitrary Lagrangian-Eulerian" method to continually smooth the mesh throughout. The modelling is not straightforward, as it involves complex surface interaction in conjunction with material confinement. It is essential to capture the strain-hardening and strain-rate effects of the polymer material within the model. A rate-dependent elastic-plastic material was found to be sufficient. The Material Law was parameterised using the free-drawing behaviour measured during a comprehensive set of tensile tests, performed over a large range of processing temperatures and speeds. Finite Element results agree well with drawing experiments, in terms of geometry, stretch ratio and drawing force. We demonstrate how simulation can accurately predict and optimise solid phase processing applications, and leads to a more detailed understanding of the conditions required to produce orientation.