Abstract: Hill's yield criterion for plastically orthotropicsolids is used to predict the yield stresses of single crystal Nickel-basedsuperalloys DD3, but the correlation to experiments at 760℃ ispoor. Taking into account the fact that the components of tensionstresses are coupled with components of torsion stresses when off-axis loads areapplied for an orthotropic material, Hill's yield criterion for plasticallyorthotropic solids is modified by adding an invariant which is composed ofthe quadratic product item of components of deviatoric stress tensor, and a newyield criterion is put forward in term of the characteristics of cubicsingle crystal material. The coefficients in the new criterion can bedetermined from uniaxial tension tests and the method of determining thosecoefficients is given in the paper. Equivalent stress and equivalent strainfor the new criterion are defined. The new criterion, newequivalent stress and equivalent strain will be reduced to the von Mises'sfor isotropic material. The correlation to experiments is very good whilethe new criterion is used to predict the yield stresses of single crystalNickel-based superalloys DD3, and it gives more accurate results than thatof Hill's at 760℃.