We propose the use of a critical tensile stress as a criterion for the onset of gross melt fracture (OGMF). This stress is estimated from the entrance pressure drop using the method of Cogswell. Carbon black tracer was used to verify that what we deemed to be GMF, based on the inspection of extrudate, was Indeed the result of a brittle rupture. An orifice die was used to eliminate the complications arising from the presence of a capillary. Polyethylenes having a variety of molecular structures were used to evaluate the usefulness of the critical tensile stress for characterizing polymers. The critical stress was found to be independent of temperature and contraction ratio. It is also independent of entrance angle, as long as this is equal to or greater than 90 degrees. The critical stress is thus a material property and can be used to rate the tendency of polymers to exhibit gross melt fracture.