The Ritz variational method was used in this study to solve the lateral torsional buckling problem of simply supported thin-walled beam with doublysymmetric cross-section. Two considered cases of loading were uniform bending moments applied at the two ends, and a point load applied vertically at the midspan. The problem was presented in variational form as the problem of minimizing the total potential energy functional, , with respect to the unknown parameters of the generalized displacement modal functions. The total potential energy functional was found to be a function of two unknown displacement buckling functions v(x) and (x) and their derivatives with respect to the longitudinal coordinate axis. Suitable displacement buckling functions that satisfy the Dirichlet boundary conditions at the ends were used as trial functions to obtain the Ritz variational problem as the minimization of  with respect to the generalized buckling modal displacement amplitudes c1n and c2n. The Ritz variational equations were obtained as the minimum conditions for  with respect to c1n and c2n. The equations were solved for the two cases considered and the buckling moments found for the nth buckling mode from solving the resulting system of homogeneous algebraic equations. It was found that the expressions obtained for the buckling moments in each considered case were the exact expressions obtained by other researchers in literature who solved using classical mathematical methods. It was further found that for each considered case the critical buckling moment occurred at the first buckling mode, and the critical buckling moment expressions for each case agreed with exact solutions from the literature. The effectiveness of the Ritz variational method was thus illustrated for stability problems of thin-walled beams with Dirichlet boundary conditions.