We study stationary vibrations and static bending of a bimorph plate consisting of two piezoceramic layers with an infinitely thin split electrode between them. We propose a model taking into account the square root singularity of the electric field structure on the interface between the split electrode regions. For the plane problem, we obtain the equation of motion and formulate the boundary conditions and the transmission conditions on the interface between the split electrode regions. For the piezoceramic PZT-4, we calculate the resonance and antiresonance frequencies and study the dependence of the dynamic electromechanical coupling coefficient on the dimensions of the internal electrode. We show that the use of a plate with a split electrode permits increasing the efficiency of vibration excitation compared with the case of a solid internal electrode. In the case of static bending of the plate-strip, we determine the dimensions of the internal electrode ensuring a significant increase in the deflection at the center of the bimorph.