An apparatus is designed for the determination of the axial pressure distributions of molten polyethylene and polypropylene, both in a capillary and in a reservoir. Experimental results reveal that the pressure at the tube exit, termed “exit pressure,” is above atmospheric and it is found to be shear dependent for a given L/D ratio. The authors suggest a modified Bagley plot corrected for “exit pressure.” Such plots show curvature at the entrance region. The plots of entrance‐correction vs. wall shear stress also show curvature, thus indicating that Hooke's law in shear is not obeyed by the polymers under study. The “exit pressure” is further used to correlate with the total pressure drop at the entry to the tube.