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This paper deals with the optimum design of composite laminated plates under stiffness and gauge constraints. A multi-objective function which combines the plate weight and the strain energy stored in the plate by weighting parameters is introduced. This objective function is minimized while satisfying constraints such as the structural deformation and the limits on design variables. Both ply orientation angles and ply thicknesses of the composite plate are used as the design variables. The stiffness analysis is performed by the finite element method in which a triangular element is used that is suitable for the analysis of thin to thick plates and includes the transverse shear effects. Analyses of the derivatives of the objective function and the constraint functions with respect to the design variables is performed analytically. The mathematical programming method called the constrained variable metric is used to solve this optimum problem. An example is provided for the optimal design of a rectangular laminated plate.