This paper describes finite-element simulations and associated experimental studies of extrudate swell for near-monodisperse and polydisperse polystyrenes. The tube-model based Rolie-Poly constitutive model, when extended to include a reduction of monomeric friction at high extension rates, makes much-improved predictions of extrudate swell at high Weissenberg number. This is especially significant for near-monodisperse polymers where rheological features are unchanged by the effects of polydispersity. Extension of this molecular rheology scheme to a polydisperse constitutive model addresses extrusion experiments on polydisperse polystyrenes inside a multipass rheometer, accounting for experimental data up to Rouse Weissenberg numbers of 50. We, therefore, show that from a measurement of polymer molecular weight distribution, it is possible to predict extrudate swell over a broad range of processing conditions for polydisperse polymers and realistic extrusion processes. Small changes in the capillary length to diameter ratio have little effect on extrudate swell in this range of Weissenberg number. This is because the capillary residence time is sufficiently long for a steady state to be reached within the polymer stretch relaxation time, which controls the most decisive physics responsible for extrudate swell. (c) 2019 The Society of Rheology.