Polymer melts and concentrated solutions rupture at high rates of elongation in a manner that is reminiscent of the cohesive failure of solids. We propose a simple molecular picture of rupture of a polymer filament, in which catastrophic failure occurs when the frictional force on an entangled chain can no longer balance the tension in the chain. The model, which is fully predictive and contains no adjustable parameters, captures the rupture characteristics of the available data sets and agrees quantitatively with critical stress critical strain data and the dependence of critical strain on the Weissenberg number. (C) 2003 The Society of Rheology.