The limit bending-radius as the main straightening technical parameter,decides the structure of equipment and the quality of products for straightening thin-walled tubes with equal curvature,however,it is usually carried out based on the experiential data and chart by skilled labourers,whose art is based on long experience and experiments,the special mathematical model of the limit bending-radius is immediately necessary. Therefore,by means of the membrane shell theory and it’s relevant hypothesis the stress-strain state is proposed firstly,and based on plastic incremental theory,the limit bending-radius model for the prediction of diffuse plastic instability under pure bending is derived using Swift’s criterion. In order to certify whether it is correct,we have done the dynamic simulation by FEA,the results have shown that the model is approximate correct,finally the influencing factors of the limit bending-radius are analyzed qualitatively,this paper can also provide the basis for optimizing straightening technical parameters and completing the theory of thin-walled tube straightening.