The true shear stress at the wall is discussed. The theoretical result suggests that Bagley's formula holds even if the exit pressure is not negligible in capillary flow of polymer melts. The importance is emphasized of distinguishing the pressure in the axial direction (driving pressure) from that in the radial direction in cases of flow where primary and secondary normal stress differences exist. Accurate experiments were carried out to confirm the theoretical result for two kinds of high‐density polyethylenes. Experimental results indicate that wall pressure, which is normal to the capillary wall, decreases rather rapidly near the entrance and then at a constant rate in the following part, while the driving pressure in the axial direction decreases at a constant rate from the beginning and the shear stress is constant throughout the capillary. We also obtained experimentally the mean normal stress difference, which is the cross‐sectional mean of the primary normal stress difference and half of the secondary normal stress difference. It was shown that the mean normal stress difference decreases gradually untilLc/D=5and remains constant thereafter. The existence of a close correlation between the mean normal stress difference and die swell ratio was found. The primary normal stress difference was obtained from the data of mean normal stress difference and the secondary normal stress difference. The pressure distributionsPzz(r),Prr(r)andPφφ(r)are discussed.