Abstract: Different shear warp displacement functions are assumed for the top flanges and bottom flanges. The energy function for the open thin-walled compress bar is obtained. Based on the minimum potential energy principle, the characteristic equation of the compress bar is derived. The critical load and the correct coefficient for Eular formula of the simple-supported compress bar are calculated. The influence of the width, the thickness of the flange and the span of the compress bar as well as the geometry nonlinearity on the corrent coefficient of the critical load is discussed. The conditions for the applications of Eular critical load formula are discussed.