A vibratory sensor is fabricated as a three-dimensional batch-micromachined shell adapted to vibrate and support elastic wave propagation and wave precession in the shell or membrane and at least one driving electrode and preferably a plurality of driving electrodes directly or indirectly coupled to the shell to excite and sustain the elastic waves in the shell. The pattern of elastic waves is determined by the configuration of the driving electrode(s). At least one sensing electrode and preferably a plurality of sensing electrodes are provided to detect the precession of the elastic wave pattern in the shell. The rotation of the shell induces precession of the elastic wave pattern in the shell which is usable to measure the rotation angle or rate of the vibratory sensor.