A theoretical investigation of initial local buckling and post-buckling behavior of composite I-sections is presented. The equilibrium equation for initial buckling is solved both exactly and with an approximate method, namely, Galerkin's method. In Galerkin's method, the out-of-plane deflection of each plate element is approximated by a weighted sum of polynomial functions. The post-buckling response is studied as an extension of the approximate analysis with Galerkin's method where now both equilibrium and compatibility equations must be solved. The bending deflection in the post-buckling regime is assumed to be a magnification of the deflection function used in initial buckling analysis. No mode-shape change is thus allowed in the post-buckling region. A polynomial type of function is also adopted for stress distribution in order to take into account the deviation from uniform in-plane load distribution in the plate elements following the onset of local buckling. The paper provides an efficient and accurate method for predicting the post-buckling behavior of composite structural sections composed of plate elements. Galerkin's method was previously applied to isotropic flat plates only. The present approach is tested against a commercial code, STAGS, with a very good agreement in results and a very large saving in computer time for post-buckling analysis of an I-section.