The elongation behavior of various polymer melts extruded from the single screw extruder has been studied. Low-density polyethylene, high-density polyethylene, polypropylene, and their short glass-fiber (GF)-filled composites were used. It was found that the spinning stability was good but the drawability was poor for GF-filled polymers. The elongation viscosity was measured by use of a Gottfert tensiometer (Rheotens) in the strain rate range from 0.1 to 4 s−1. In regard to the viscosity calculations, a very convenient and straightforward method, especially for molten materials without die swell, is presented. All the sample melts showed slight tension thinning; that is, the elongation viscosity decreased along with the strain rate. It was also found that the elongation viscosity of the GF-filled polymer may increase along with the fiber content up to a critical value, and then drop if more fiber is added. The influence of the die geometry on the viscosity measurement is discussed.