This article focuses on the development of a two-axis solid state micro gyroscope (SMG) on surface acoustic waves (SAW). The described gyroscope belongs to the category of inexpensive sensing elements featuring a high degree of longtime overload stability. This advantage seems to make SAW SMGs a priority choice for navigation and control systems functioning in severe overload environments of up to 65,000 g. As of today SAW SMGs are designed according to a number of known principles. Such SMGs may also operate on standing SAWs or traveling SAWs. This article addresses the first gyro type. Unfortunately, the existing standing SAW SMGs share a common limitation of measuring angular rates in relation to one axis only. This research attempts to introduce an innovative two-axis standing SAW SMG. The influence of the basis rotation on the parameters of the elastic waves traveling within the substrate layer was carefully studied. Incident and reflected wave models were also elaborated. The numerical simulation results demonstrate the effects of the basis rotation on the complex factors of the volume waves reflected by the substrate layer and on the phase velocity and frequency thereof as well as on the oscillation amplitude of the particles involved in SAW transition, and on the elliptical particle movement path configuration. Also, the SAW SMG is compared to the existing micromechanical gyroscopes, and the basic SAW SMG production technologies are reviewed. © 2019 New Technologies Publishing House. All right reserved.