The capillary flow properties of two commercial samples of polystyrene(Mw/Mn≈2.5–3.0)and three narrow distribution samples(Mw/Mn≈1.1)have been examined. Viscosity and extrudate diameter were measured as functions of temperature, shear rate, capillary diameter, and capillary length. Shear stress was found to be the primary flow variable controlling the swelling ratio (extrudate diameter/capillary diameter); polydispersity was the primary molecular variable. At low shear stresses the swelling ratio in all samples approached a constant value of approximately 1.10, concomitant with the approach of the viscosity to its Newtonian value. At high shear stresses the first normal stress difference,P11−P22,was calculated from the swelling ratio by the momentum balance method of Metzner et al. The values obtained were too small by several orders of magnitude. An alternative approach, in which the increase in diameter at the exit was attributed to stored elastic energy in the fluid, led to normal stresses of the correct magnitude.