In this paper, the lateral-torsional and distortional buckling stability of rafters with elastic supports subjected to gravity loads have been studied by means of a numerical method. To fulfill this purpose, the equilibrium equations for elastic rafter members with linear behavior are derived from the stationary condition of the total potential energy. In the applied energy method, effects of initial stresses and load eccentricities from centroid of cold-formed cross-sections are also considered. The Power series expansions are utilized to solve the fourth-order differential equations of considered rafters with variable coefficients. According to aforementioned method, displacements components and geometric properties are approximated by power series form with a known degree. The critical buckling loads are then derived by solving the eigenvalue problem. In order to present the accuracy of the proposed method, several numerical examples including lateral-torsional behavior and distortional buckling analysis of rafters with cold-form sections are considered. The evaluated results are compared to the finite element simulations and other available methods.