Abstract: Whitney's lemma is an important theorem in local singularity theory of germs of C  functions.In this paper,we are going to prove the global version of this lemma.Based on this generailized theorem and the relevant conclusions in singularity theory,the plastic yield criteri- on is discussed in detail.We found that the most general form of the plastic yield criterion should be f(J₁T2,Js)=0.Obviously,this form is more precise than the form f(J₁,J₂,J₃)=0 which is given in the usual literature.Finally,we shall also give some practical examples for explanation.