Equations for linear piezoelectricity are formulated in a reference frame rotating at a constant angular velocity and are simplified by a perturbation procedure when the angular velocity of the reference frame is small. The equations thus obtained are then employed in the analysis of a rectangular ceramic plate piezoelectric gyroscope operating with thickness shear modes. Approximate analytical solutions to the equations resulted from the perturbation procedure are obtained based on Mindlin’s two-dimensional equations for a piezoelectric plate which are simplified by the thickness shear long wave approximation. Free-vibration frequencies and mode shapes, as well as the condition for double resonance, are obtained. Forced vibration is also studied which leads to a simple expression for the voltage sensitivity of the gyroscope. The analysis is approximate and qualitative mainly with the purpose of exhibiting some most basic characteristics of the gyroscope. Some of the results are compared with finite element numerical method.