In order to find the optimum design of structures that have characteristic natural frequency range, a numerical optimization method to solving eigenvalue problems is a widely used approach. However in the most cases, it is difficult to decide the accurate thickness and shape of structures that have allowable natural frequency in design constraints. Parallel analysis algorithm involving the feasible direction optimization method and Rayleigh-Ritz eigenvalue solving method is developed. The method is implemented by using finite element method. It calculates the optimal thickness and the thickness ratio of individual elements of the 2-D plane element through a parallel algorithm method which satisfy the design constraint of natural frequency. As a result this method of optimization for natural frequency by using finite element method can determine the optimal size or its ratio of geometrically complicated shape and large scale structure.