A straight, slender beam with elastically restrained boundaries is investigated for optimal design of an intermediate elastic support with the minimum stiffness for the purpose of raising the fundamental frequency of the beam to a given value or to its upper bound. Based on the optimality criterion of the support design, the characteristic frequency equation can readily be formulated. Then, a closed-form solution is presented for estimating the minimum stiffness and optimum position of the intermediate support such that the analysis of the various classical boundary conditions is only a degenerate case of the present problem. With the procedure developed, the effects of the general cases of the beam restraint boundaries on the optimal design of the intermediate support are studied in detail. Numerical results show that the optimum position will move gradually apart from the end with the degree increment of the boundary restraints. Moreover, it is also observed that the rotational restraint affects the optimal design of the support more remarkably than the translational one at the lower values of the restraint constants, but becomes less effective at the higher constants.