The minimum weight design of laminated composite plates subject to strength and side constraints is studied via a constrained global optimization technique. The first-ply failure load that is treated as the strength of a laminated plate is determined by using a shear deformable finite element and one of the several commonly used phenomenological failure criteria. The optimal layer group parameters (fiber angles and thicknesses of layer groups) of the laminated composite plate are determined via the proposed constrained global optimization technique for attaining the global minimum weight of the plate and satisfying the imposed constraints. A number of examples of the minimum weight design of symmetrically laminated composite plates with various aspect ratios, different number of layer groups, and different boundary conditions are given to illustrate the applications of the present constrained global optimal design method. The effects of the failure criteria on the optimal design parameters are also investigated via the examples. Finally, experimental investigation of the capability of the present method in obtaining global optima is performed. Failure tests of a number of graphite/epoxy laminates designed by different methods are performed, and the superiority of the present method over the other methods is demonstrated via the test results.