Ever since the so-called slip theory was proposed by Batdorf and Budiansky in 1949, it has become a subject of discussion and is not yet settled which of the theories should be valid, the slip theory or the incremental strain theory. In the present paper, the characteristic shear function introduced by them is computed for the two fundamental loading processes, tension and torsion of circular tubes, and accordingly it is shown that the function assumes different values in each case, consequently that the slip theory is invalid.