The transfer stiffness coefficient method is applied to a thin plate structure which is constructed by combining a number of rectangular plate elements in series. Each plate elements is equally divided into some rectangular fundamental elements, and is reconstructed by connecting the fundamental elements according to parallel and series transmission rules. In this process, the inner degrees of freedom of the plate element are completely eliminated by an efficient internal computation rule. An algorithm based on the present method is formulated for in-plain and bending free vibration analyses of a flat plate structure. The validity of the present algorithm concerning the computation efficiency, the computational accuracy and the memory requirement is confirmed by comparing the numerical computational results obtained by the transfer stiffness coefficient method with those obtained by applying the finite element method.