This paper describes a method of finding the elastic constants of a generally orthotropic composite thin plate through modal analysis based on a Rayleigh-Ritz formulation. The natural frequencies and mode shapes for a plate with free-free boundary conditions are obtained with chirp excitation. The characteristic functions of vibrating beams have been assumed for the plate deflection in developing the eigenvalue problem. Based on the eigenvalue equation and the constitutive equations of the plate, an iteration scheme is derived using the experimentally determined natural frequencies to arrive at a set of converged values for the elastic constants. Four sets of experimental data are required for the four independent constants: namely the two Young's moduli E1 and E2, the in-plane shear modulus G12, and one Poisson's ratio V12. The other Poisson's ratio v21, can then be determined from the relationship among the constants. Comparison with static test results indicate good agreement. Choosing the right combinations of natural modes together with a set of reasonable initial estimates for the constants to start the iteration has been found to be crucial in achieving convergence.