Abstract: The critical curvature-radius, as the main technical parameter in strengthing, 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 experiential data and charts by skilled labourers, whose art is based on long experience and experiments, and as such a specialized mathematical model is immediately necessary. Therefore, applying the large deflection strain-displacement relations of the shell of revolution, the mechanical model of the critical bending-moment for equal curvature straightening is presented by the Ritz method, based on J₂ deformation theory and energy methods. Then the critical radius is subsequently derived and it is also shown how to solve for it synchronously. In order to certify whether it is correct, several dynamic simulations were performed in ANSYS/LS-DYNA, and the results have shown that the model is approximately correct. By comparison of the simulations' results it is shown that wrinkling on the compression side of the tube occurs before buckling and is the principal failure mode when straightening plastically-unstable thin-walled tubes with equal curvature.