Composite materials have been mostly used in engineering applications such as aerospace, automotive, sports equipment, marine because of their high specific strength-to-weight and stiffness-to-weight ratios. Weight reduction and buckling load capacity are critical issue for the engineering application. Accordingly, in this thesis, identification of optimum fiber orientations and laminate thicknesses of the composite plates resisting to buckling under given loading conditions and aspect ratios are investigated. Furthermore, a comparison study on continuous and conventional designs is performed to determine the effect of stacking sequence on weight. Symmetric and balanced N-layered carbon/epoxy composite plates are considered for optimization process. Critical buckling load factor is taken as objective function and fiber orientations which are considered continuous are taken as design variables. Simulated Annealing (SA) algorithm is specialized by using fmincon as hybrid function and this optimization method is used to obtain the optimum designs. Maximum critical buckling load factor and minimum thickness and hence minimum weight are achieved and shown in tables. As a result, it is observed that loading conditions and plate dimensions play an important role on stacking sequence optimization of lightweight composite laminates for maximum buckling load capacity.