Abstract: By introducing two displacement functions and two stress functions, two independent state equations are constructed based on the three-dimensional piezoelasticity equations for transverse isotropy. The original differential equations are thus decoupled with the order reduced that will facilitate obtaining solutions of various problems. For the simply supported rectangular plate subjected to bi-axial uniform pressures, two relations between the state variables at the top and bottom surfaces are established. In particular, it is found that there exist two independent classes of stabilities. The first class corresponds to the purely in-plane stability and the second to the general flexural stability. Numerical examples are finally presented and the effects of some parameters are discussed.