The energy method for analyzing piezoelectric ceramic transducers [B. S. Aronov, J. Acoust. Soc. Am. 117, 210–220 (2005)] is applied to the treatment of transducers with mechanical systems that can be considered as two‐dimensional. Analysis is made following the general outline of the theory of coupled vibration in two degree‐of‐freedom systems and its extension to calculating resonance frequencies of elastic bodies, as suggested by Gibbe and Blechshmidt [Ann. Phys. 18, 417–485 (1933)]. The approach to the problem is illustrated with examples of piezoelectric rectangular plates, stripes, and thin‐walled cylinders at various orientations relative to crystallographic coordinate system. For all of the examples, the resonance frequencies and effective coupling coefficients are presented as functions of the dimensional aspect ratios. Equivalent electromechanical circuits are introduced, which permit calculation of the transducers performance under different acoustical loading conditions. Practical recommendations for improving the electromechanical properties of the transducers by use of appropriate aspect ratios are discussed.