The design of a two-axis micromechanical angular rate sensor based on a vibrating gyroscope of R-R type is presented in this paper. The gyroscope is built with the use of “sandwich” scheme, which uses the magnetoelectric exciter of torsional oscillations of a silicon sensitive element, two feedback loops on measurement channels consisting of capacitive pickoffs, amplifiers and magnetoelectric torquers (MT). Design features of the device provide its operability in gas-filled chamber at atmospheric pressure. Digital systems designed for the resonance tuning of the device and the maintenance of constant amplitude of angular rate of pendulum oscillations are described. The systems compensating the device zero bias and generating the output signals based on the microcontroller are also considered. The reasons for occurrence of gyroscope zero bias, connected with manufacturing defects of torsional pendulum elastic suspension and magnetic systems, are analyzed, and recommendations are given for their compensation by using such procedures as adjusting magnetic system of the exciter of torsional oscillations, modifying the elastic elements and introducing a compensating signal in a feedback loop. The results of calculating an elastic micromechanical system, modeling a gyroscope motion are presented in the paper at various ways of forming a feedback loop, as well as results from experimental research of the micromechanical angular rate sensor under development.