In this contribution the various rupture mechanisms which can occur during the elongation of polymer melts will be briefly reviewed, with the focus on the cohesive brittle melt rupture. Observations of melt rupture phenomena during polymer processing operations will be discussed. The occurrence of brittle melt rupture is characterised by a constant value of the rupture stress in the older of 1 MPa. Published rupture stress data on various polymer melts are critically discussed, in particular those on polyethylenes and other polyolefins. Using the Rheotens technique a newly developed method will be described to measure the melt rupture str ess of polypropylene (PP) melts. The measurement of the rupture stress of PP melts is hampered by the occurrence of the instability draw resonance. This problem was overcome by applying more pronounced cooling conditions. Initial data on the rupture stress of PP melts will be presented. It is shown that the rupture stress of PP melts is not a constant but increases with increasing molecular weight.