The buckling and post-buckling analyses of a compression member with a lateral bracing with eccentricity were performed, considering the elasto-plastic behavior of the compression member with a elastic lateral suport. The results obtained are as follows: 1) If the bracing stiffness is larger than 2.0 Kco(basic stiffness), bracing force is smaller than 2% of the maximum strength of the compression member, expect for the long compression members having large eccentric bracing, at the buckling stage. 2) At the post-buckling stage, the lateral bracing force increases with the increase of the buckling deformation. The necessary stiffness and strength of the bracing increase, as the eccentricity of the bracing increases.