The basic problem in polymer melt elongational rheometry is obtaining a stable and constant elongational flow field free from shear effects. The objective of this study is to present a technique to generate elongational flow of polymer melts in a converging channel. The results of the study included the development of numerical solutions for flow behavior in the coextrusion of a core polymer melt encapsulated by a sufficiently low viscous skin polymer melt for linear and converging die geometry. In the converging geometries, it was possible to generate nearly pure elongational know in the core by choosing an appropriate skin material.