Abstract: A given length thin-wall member, under axial or lateral loads belowits material limit strength, may under go elastic flexural and torsional buckling. An analysis is carried out for the I-section cantilever steel beam in this paper.Equilibrium method and energy method are used to obtain the differential equationof the elastic flexural and torsional buckling under the axial pressures andtransverse loads, and Ritz method is used to solve the derived differentialequation and obtain critical values and the limit characteristics ofthe fixed beam section.