Abstract: This paper takes the solution of a plate with two opposite edges being shearfree-clamped as the initial solution. By eliminating the restrained edge moments successively, the solution of the original plate is obtained. To simplify this iteration, an approximation of the edge moment is introduced and the infinite number of iterations is reduced to one single calculation. The computation is then simplified greatly and the complicated work in solving large system of simultaneous equations or infinite number of iterations is avoided. Therefore only a minimum of computer memory is required. In whole calculation procedure, only single Fourier series is used and the accuracy of the computation is easily controlled. The accuracy and applicability of the suggested menthod was checked by comparison with other author's results.