Optical phase modulation in a standard telecommunication fiber coated with a piezoelectric ZnO jacket has been investigated both experimentally and theoretically, The frequency response of the modulator exhibits 18 peaks between 20 and 800 MHz, which correspond to radial resonances of the coated fiber composite, A theoretical model was developed to explain the experimental results, The model takes into account the geometry of the modulator, nonuniform strain distributions, and the structure of the ZnO film, The calculated positions of the resonances and cancellation of phase modulation at frequencies higher than 800 MHz agree well with the measured data. The analysis also demonstrates the capability of tuning the resonances positions by varying the thickness of the ZnO jacket or the metal electrodes.