Abstract—An anisotropic form of the Von Mises yield criteria is presented which includes linear terms and therefore enables Bauschinger effects to be considered when constructing yield or loading surfaces.The coefficients representing the state of anisotropy are expressed in terms of the uni‐axial and shear yield stress of the material. It is suggested that this form of the yield or loading surface can be used to determine the plastic strains for a range of multi‐axial and cyclic plasticity problems and results are presented for the particular case of a tube subjected to cyclic plastic torsion with an axial s