Abstract: Apart from the special case of a simply supported Ⅰ-beam Subjected to uniform moment where a closed form solution is available,most of the buckling loads were obtained by numerical methods. In the present paper a closely approximation for lateral buchling of simply supported Ⅰ-beam is proposed by using Galerkin's method of weighted residuals. The results and the predichons by experiment, and theoretical, optimal, finite element, and ect analyses for the lateral buckling loads are to agree well in all the four examples. The results from these comparisons show that the Proposed formula here is capable of quickly and efficiently predicting the lateral buclding of simply supported thin-walled member. The fast convergence of the results indicates the numerical stability of the method, and by the Study of conuergence, a very complex practical eigenvalue problem is transformed into a very simple of solving only a linear equation with one variable.