A simple model of a polymer melt has been offered to explain the normal stress effect and the Barus effect in case of a steady shear flow. Assuming that a polymer melt consists of numerous flowing units which in turn are aggregates of radial Voigt elements with balls at their outer ends, the primary normal stress difference and swelling ratio were calculated theoretically. The experiments were carried out to test the theory. The exit pressure and swelling ratio were measured in cases of two high‐density polyethylenes, a polypropylene, and a low‐density polyethylene. The primary normal stress difference was calculated from the measured exit pressure. Insofar as our experiments are concerned, the theoretical results show reasonable agreement with the experimental results in both cases of the normal stress effect and the Barus effect.