An analysis is presented which shows how the theory of anisotropy based on a von Mises criterion of yielding first proposed by Hill may be extended to the plastic torsional straining of a hollow cylinder. Expressions are given for the anisotropic parameters, and the yield stresses along the anisotropic axes in terms of certain quantities, namely; the change in axial and tangential strain with shear strain, the principal yield shear stress, and the through thickness yield stress of the hollow cylinder. Experimental measurement of these quantities is made for the plastic torsional straining of hollow cylinders of A1-1100. Experimental data are analyzed using the previously derived expressions, and the anisotropic parameters, and yield stresses along the anisotropic axes determined. Finally, the results of the investigation are discussed, and conclusions drawn.