Experimental results for twenty-five tubular specimens of a 24S-T-4 aluminum alloy, subjected to combined torsion-tension-reversed torsion, are reported in a study of the initial and two subsequent yield surfaces covering the first and the fourth quadrant of the axial stress-shear stress plane. Results are also given for two additional specimens subjected to tension followed by torsion, in order to compare the values of the initial shear modulus at the initiation of twist with the elastic shear modulus.