Abstract: The correlation of crystal orientation to yield characteristic of FCC single crystal is not good when Hill's (1948) yield criterion is used to describe the elastic-plastic deformation of FCC single crystal.Taking into account the effects that the components of tension stress are coupled with components of torsion stress when off-axis loads are applied to orthotropic material,Hill's yield criterion for plastically orthotropic solids is modified by adding an invariant which is composed of quadratic product item of components of deviatoric stress tensor,as a results,a new yield criterion for single crystal Nickel-based superalloy is put forward in the present paper in terms of the characteristics of single crystal Nickel-based superalloy.Using the new criterion to predict the yield stresses of single crystal Nickel-based superalloy DD3,the correlation to experiments is very good and more accurate than that of Hill's at 760℃.Equivalent stress adapted to the new criterion is defined.Thinking of the yield function as a plastic potential function from the associated flow rule and with reference to the isotropic hardening model,the elastic-plastic constitutive model for single crystal Nickel-based superalloy is constructed and the corresponding elastic-plastic matrix is educed.New yield criterion and its equivalent stress will be reduced to Von Mises yield criterion and corresponding equivalent stress for isotropic material.