Abstract: Based on Ježek method of computing elastic-plastic buckling of member under the axial compressive load and bending moment, analytical expressions of calculating ultimate load of buckling about neutral axis with maximum moment of inertia for a rectangular column with its upper and lower surfaces wrapped by carbon fibre are derived. The results obtained by the formulae are in good agreement with finite element solution, which provide a new method of theoretical study for elastic-plastic buckling of member. The example shows that the more region of the member section yields, the greater the reinforcing action of carbon fibre is. It is believed that gluing carbon fibre on the surface of steel member may significantly increase its carrying capacity of elastic-plasticity.