The principal operation of a ring laser gyroscope depends on the phase difference for the counter-propagating waves within a closed path. The reflection mirrors mounted on the resonator block form the traveling waves. Thus, the dimension accuracy of resonator block influences the traveling path of beam. In order to maintain the stable optical beam path in the ring resonator, the piezo-driven moveable mirror is adopted for the path length control under the thermal expansion or mechanical strain of resonator block. This paper presents the mathematical description of the elastic behavior of piezo-driven mirror. This description can be applied for the concept design of piezo-driven mirror. For the beam path control due to a piezo-driven mirror, this paper presents a theory of deflection of piezo-driven mirror as a function of the geometries and material properties of mirror components. In comparison with the simulation of finite element model, the theoretical result has the feasible error tolerance. If the effective geometries on the base of deformation can be taken into account, the more precise result can be calculated. But through the comparison, the presented theoretical approaches are known to be available.