In recent years, fiber-reinforced composite materials have been increasingly used in engineering applications due to their advantages such as strength and weight reduction. Determination of the buckling load capacity of a composite plate under in-plane compressive loads is crucial for the design of composite structures. Accordingly, in this thesis, optimum designs of anti-buckling behavior of 64-layered carbon/epoxy composite plates, which are simply supported on four sides and subject to biaxial compressive in-plane loads, are investigated considering Puck failure criterion by using genetic algorithm (GA). The plates are taken to be symmetric and balanced with continuous fiber angles in the laminate sequences. Critical buckling load factor is taken as objective function and fiber orientations are taken as design variables. The critical buckling load factor is maximized for various loading cases and plate aspect ratios. The optimum designs obtained are controlled layer by layer using Puck failure criterion. A comparison between continuous and discrete plate (laminate in which the orientation angles are limited to the conventional orientations) designs is performed in order to show the reliability of continuous plates. The optimization of 48-layered composite plates has been performed in order to be compared with 64-layered composite plates. The optimum designs considering Puck inter-fiber failure mode C has also been investigated. Finally, a comparative study between Puck and Tsai-Wu failure criteria is performed and the advantage of Puck failure criterion is shown. In conclusion, it is found that the optimum designs of laminated composites considering buckling and ply failure strength depend on loading, loading ratio and plate aspect ratio.