In the previous papers, a relatively rigorous theory was presented with respect to the elasto-plastic behaviours of bi-axial bending beam-columns. An aproximate analysis deals with the same problem as above and a relatively simple interaction formula is proposed for the maximum values of forces and bi-moments. The formula simultaneously takes into account the danger of plastic collapse by bending and that of buckling by torsion-bending. It gives safety with respect to the results of theory and those of tests.