Abstract: The conditions necessary for verification of the upper and lower limit theorem,which have been now verified,were analyzed.It was believed that there were still disputable points deserving of further elaboration in the verification that had been so far made.It was demonstrated that the stress relationship in the method of characteristics was identical with the yield condition defined in this paper and the conditions for extreme values of the yield function,on such a basis,a rigorous verification was made for the theorem.A new flow rule was recommended,and it offered a new way for obtaining the approximate solution of the ultimate load with the theorem.