Abstract: The differential equations governing the buckling behavior of axially compressed members describe three buckling modes in the elastic region： flexural buckling， torsional buckling， and flexural-torsional buckling， providing a theoretical foundation for design codes. This paper systematically presents the design formulas for flexural， torsional， and flexural-torsional buckling of axially compressed members under both the 17 steel standard and the American steel standard， with the stability coefficients for all three modes being derived from the flexural buckling column curve.