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This paper proposes optimal design of frame structures for vibration suppression in mechanical systems. The H∞ norm of the transfer function from disturbance sources to the output points where we have to suppress vibration, is adopted as the objective function to represent the magnitude of vibration transfer. The design parameters are the cross-sectional areas of frame members. For minimization of the H∞ norm under a constraint of the total mass, a gradient method is employed, where the gradient vector is computed from the variation of H∞ norm for small changes of cross-sectional areas satisfying the mass constraint. Examples are presented to demonstrate the effectiveness of the proposed design method.