Vibratory gyroscopes are now most applicable for such intelligent systems as drones, for motion stabilization, robots for accurate positioning of end-effectors, virtual reality systems to change image orientation with turn of a head and many others. During motion these systems can be exposed to mechanical shocks and vibrations. To provide required accuracy, working in such environmental conditions, gyroscopes shall have property of robustness to operating disturbances. This paper proposes differential mode of operation for single-mass vibratory gyroscope as a new operating mode that has higher rejection factors for different external disturbances like shocks and vibrations allowing meeting the requirements of many important applications in intelligent systems. Test results presented in this paper show excellent disturbance rejection properties of differential mode of operation in comparison to well-known rate mode. Despite excellent disturbance rejection results have been obtained for non MEMS gyro, the same results can certainly be obtained for MEMS gyro, too.