An applied theory of cylindrical bending vibrations of a bimorph plate is developed, which takes into account the nonlinear distribution of the electric potential in piezoelectric layers. Finite-element analysis of this problem showed that such distribution arises when solving the problems of finding the resonant frequencies and modes of vibration or in the case of forced oscillations during their mechanical excitation, when the electric potentials on the electrodes are zero. The quadratic distribution of the electric potential adopted in the work showed good consistency of the results with finite-element calculations for natural oscillations and steady-state oscillations for a given potential difference when the electric potential distribution is close to linear.