Predictions of the exponential shear stress coefficient by the Curtiss‐Bird and Giesekus theories for polymer melts are presented and compared. Whereas these two theories give very different predictions for uniaxial elongational flow, their predictions in exponential shear flow are very similar. Although both exponential shear and uniaxial elongation are “strong flows,” it appears that the strong aligning nature of the latter leads to the differences between the predictions of the two molecular theories. It is concluded that exponential shear flow has great potential for testing mean field molecular theories for polymeric liquids.