Failure of polymer liquids under flow has been the subject of a relatively strong computational, theoretical, and experimental effort over the years, despite which a clear picture of the phenomenon is still nonexistent. For example, there are still arguments in the literature whether the maximum in engineering stress, also known as the Considere limit for failure, is a point of true yielding of the polymer network or simply a purely elastic mechanical instability and if this onset of yielding also corresponds to the true onset of non-homogeneous deformation, as expressed for example by necking. The main objective of the present work is to contribute to the ongoing discussion on this matter by studying a linear polyisobutylene melt in terms of its failure and rupture behavior in both the viscoelastic and purely elastic deformation regimes of deformation showing that homogeneous flow still occurs after the maximum in engineering stress and quantifying this deviation. This is ultimately connected with the observation of a limiting stress at rupture in the rubbery (elastic) regime. From the results, it is apparent that, for this particular polydisperse melt and in the viscoelastic regime, the Considere criterion underestimates by approximately 60% the point of onset of non-homogeneous deformation, i.e., necking. The calculated true onset of failure, on the other hand, agrees almost exactly with the visually determined onset. However, it is clear that a general working criterion for failure of entangled polymer melts, especially in the all-important viscoelastic deformation regime, is still lacking. (C) 2010 The Society of Rheology. [DOI: 10.1122/1.3378791]