In this work, we present a one-dimensional, simple model to describe extrudate swell manifested by polymeric liquid emerging from a circular die. The formulation established herein can accommodate in the process of swelling all such effects as inertia, cooling and crystallization, air drag, gravity and stretching for polymer fluid with discrete relaxation spectrum. In order to take flow history inside the die into consideration, we employ assumed concept for force flux balance that transforms stress field in shear into that in extensional flow at the die exit. This approach is expected to be applicable to several other polymer processing operations. A few comparisons with experiments for polyisobutylene and polyethylene are presented, and they show that the developed procedure yields good description of the data for both cases of free swelling and stretching of extrudate. Finally, application of the theory to modeling of fiber melt spinning process from slow to high speed is demonstrated, including all such effects as non-iso-thermality, air friction, take-up, inertial and gravity forces, and hence it shows the applicability of the present formulation to some industrial polymer processes.