The subsequent yield function previously proposed by one of the authors is modified by introducing the fourth rank tensor of anisotropic moduli. This yield function accounts for the effects of the third deviatoric stress invariant and anisotropy and the Bauschinger effect. Multiaxial loading tests are carried out on tubular specimens of mild steel subjected to various amounts of torsional prestrain. Two modes of loading are used to assess the theoretical predictions: one is the combined tension- torsion and the other is off-axis torsion by means of the combined loading of compression, internal pressure and torsion. The equi-strain loci and strain behavior are examined as a function of prestrain at three levels of offset strain ranging from 0.002% to 2.0%. In the tension-torsion stress field, the equi-strain locus specified by a 0.002% offset forms a nose in the prestress direction and flattens on the opposite side. The locus expands with increasing offset strain, so that both the sharpness of nose and the degree of flattening decrease. The deviation between the directions of the principal shear stress and principal shear strain increment is determined from the off-axis torsion test. It rises to a maximum value with a change in the principal shear stress direction and then decreases. The maximum deviation is larger when a smaller offset strain is used, and it increases as the prestrain becomes larger. Such behavioral characteristics can be expressed precisely by the constitutive equation derived from the proposed yield function, hardening law and associated flow rule.