In this paper, we applied the equivalent elastic constants derived by the apparent elasticity method. We studied the coupled vibrations of sandwich transducers used in high power ultrasonic, obtaining the frequency equation for the transducer design and calculation of its resonance frequency. The transducer consists of metal head and metal tail with circular cross-section, two piezoelectric ceramic rings and metal central bolt. Theoretical analyses show that the apparent elasticity method was simple, easy to calculate and especially suitable for the study of coupled vibrations. It is shown that the calculated resonant frequencies according to the apparent elasticity method provide better approximation of the measured results than those from onedimensional theory.