This paper deals with the optimum design of fibrous laminated composite plates. The plates are subjected to any concentrated and/or distributed loads and they are optimized under the constraint that the strain energy or the maximum deflection of the plates is minimized for the given thickness. The design variables are the fiber orientation angles of the small sections of the plates. Thus, the optimum fiber orientation becomes curvilinear. The deflection analysis is performed by using the Rayleigh-Ritz method and the complexity in developing the analytical formulation for the sectional plate is reduced by using the symbolic calculation system, Mathematica. The optimizer has a SUMT-type algorism. The calculated results show that the laminated plate with the sectionally-optimized fiber orientation angles yield a considerable improvement in the strain energy and maximum deflection.