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A method is presented for the optimum design of structures which is very robust and efficient in terms of the number of required analyses of the structure. Some explicit approximation expressions are generated for the structural response quantities such as nodal displacements, forces and frequencies as functions of the cross-sectional properties. By substituting these expressions into the constraint equations, the design task becomes a non-linear programming problem which is an explicit problem in terms of the design variables. The solution of this problem gives the actual cross-sectional dimensions. The method is an iterative technique and the results indicate that the convergence to the optimal solution results indicate that the convergence to the optimal solution is very rapid. The robustness of the proposed method is due to the generation of explicit approximate relations for the structural response quantities, as in the past the design constraints were approximated. Also a high quality approximation is obtained for the internal forces directly without using the approximate values of the displacements. The quality of approximations is enhanced by expressing the structural responses, in particular, the frequencies with respect to the cross-sectional areas and second moment of inertias instead of using the cross-sectional dimensions. A double-layer grid and a grillage are chosen as test cases, the results of which are presented.