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This paper proposes the use of a simulated annealing (SA) approach to the optimal design of multilayered composite plate structures. The orientation fibres and the number of layers in laminated composites play a major role in determining strength and stiffness. Therefore, the basic design problem is to determine the optimum stacking sequence of the composite laminate. The SA technique is employed to obtain the optimum fibre orientation of multilayered composite plates, so as to maximize fundamental natural frequency. The composite plate is discretized and analysed by a finite element (FE) analysis procedure using a computer program written in C language. The inverse iteration method is employed to obtain the fundamental frequency of a laminated plate with a given number of layers and fibre orientations in each layer. Both symmetric and antisymmetric fibre angles are considered. The optimum results of fibre orientations are compared with the conventional random walk (RW) method.