Abstract: In order to establish the calculation theory of flexural buckling critical loads for axial compression members under normal conditions, First of all, the total potential energy equation for bending buckling of bars was derived, then the critical loads for four kinds of end constraint conditions were obtained by employing Rayleigh-Ritz method and based on the principle of potential energy stationary value theory, and the formula of critical load amplification coefficient was given by comparing the Euler's critical load, which was able to consider the influence of slenderness ratio, compression deformation, shear deformation and cross-sectional shape coefficients, and the formula was derived in this paper can be used to calculate the critical loads for compression bars in possession of smaller slenderness ratio. The analysis of the critical loads between the circular-section and the biaxial symmetric I-section axial compression members show that the slenderness ratio of the member is the dominant factor affecting the amplification coefficient.