In this paper, a two-level decomposition method for optimal design is described. Using this method, an optimal design problem is decomposed into several subproblems in the first-level and a coordinating problem in the second-level. In the first level, the subproblems are analyzed using the global monotonicity concepts, then in the second level the analyses of the subproblems are coordinated to obtain the optimal solution. Two engineering design examples, namely a gear reducer (formulated and solved in the literature) and a flywheel (formulated and solved here), illustrate applications of the developed method.