Abstract: The ultimate bearing capacity of curved beams is related withthe bending- torsion strength and the stability.With elastic-plastic deformation, the bendingstress and the torsion stress are not linear with respect to the strain, so the problem will be more complicated.In this paper, using different formulae of the ultimate capacity of curvedbeams, a regression model is obtained. Through the nonlinear regressioncalculation for a lot of computational results obtained by using the finiteelement method, a simplified and useful calculation formula is proposed,which can be used in the practical design of the curved beams.