Abstract: A theoretical design, followed by optimization, of the amplitude transformer was carried out, which had longer small end for driving metal bonded diamond wheel with large size and heavy mass, to solve the problem of acoustic system design in ultrasonic vibration assisted ELID compound internal(UAEI)grinding of hard & brittle materials such as ceramics.Based on the propagation law of elastic wave in the medium, the value selection scheme of the amplitude transformer was determined by MATLAB, and then the scheme that met the requirements was selected according to both processing requirements and ANSYS modal analysis.Then the zero order algorithm was used to further optimize the processing, and the size of the amplitude transformer that met the requirements of geometric size, stress and vibration frequency was obtained.The vibration characteristics of the designed amplitude transformer are tested, whose resonance frequency error is within 0.192% to 1.824%, satisfying the expected design requirements.The machining characteristics of the developed UAEI grinding system are tested and compared with those of ELID.The surface roughness of the workpiece is reduced by 44.2%, and that the 3D shape of the workpiece is more flat with improved surface of the grinding wheel.