Abstract: For a thin-walled box column with variable cross-section,the three governing equations for torsional-flexural buckling are ordinary differential equations of the second or fourth order with variable coefficients,so it is very difficult to solve them by means of an analytic method.In this paper,Polynomials are used to approximate the geometric properties of cross-section and certain coefficients of the differential equations.Based on the energy principle and the Galerkinc's method,the approximate formulas for calculating the flexural and torsional buckling loads of this kind of columns are developed respectively,and numerical examples are used to verify the correctness of the solutions obtained. The results calculated in this paper provide the basis for demonstrating the stability of thin-walled box columns with variable cross-section.This paper is of practical value.