A method is proposed for minimizing the sound radiation of a vibrating beam by patterning the beam with a series of cylindrical dimples such that one or more of the vibration modes have the same shape as the corresponding weak modes. In implementing the proposed approach, the objective is to minimize the shape difference between the vibration mode(s) and the designated weak mode(s) rather than to minimize the radiated sound power at a specific frequency or over a certain bandwidth. The design objective is achieved by calculating the weak modes of the beam using the finite element method and then applying an optimization scheme with the modal assurance criterion (MAC) as the objective function. The optimization results, which cause the vibration mode(s) of the dimpled beam to approach the corresponding weak modes(s), determine the dimple angle and dimple depth. The numerical results show that the radiation efficiency of the optimized dimpled beam using MAC as the objective is generally lower than that of a uniform beam. However, the effectiveness of the proposed design strategy depends on the degree of closeness between the shape of the vibration mode(s) of the dimpled beam and that of the designated weak mode(s).