A criterion for the maximum radiated power delivered by a high‐efficiency piezoelectrically driven free disk, vibrating in the first symmetrical mode, has been developed. The maximum power emitted from such a transducer is necessarily limited by maximum stresses and strains to which the disk is subjected when undergoing transverse vibrations. A complete solution of the stress and strain distribution is given for this mode of vibration. Maximum values for these stresses and strains occur at the center of the vibrating plate. Assignment of a safe stress level, dependent on material, which the center of the vibrating plate must not exceed, then yields a unique value of maximum center velocity at which disk fracture occurs. The maximum power criterion is then established by the maximum safe center velocity, which is shown to be independent of plate geometry, and the radiation resistance of the disk in its operating medium. Experiment shows, as anticipated, that fracture occurs at the geometric center of the vibrating plate, with power values consistent with the theory.