A piezoelectric unimorph transducer consists of piezoelectric and metal discs and operates in a bending vibration mode. It is widely used in underwater acoustics and air-coupled ultrasonics. However, as the thickness of the plate increases, the transverse shear strain and its associated coupling effects cannot be ignored, especially for plates with a thickness above the medium range, where the Kirchhoff thin plate theory is no longer applicable. To precisely investigate the electromechanical characteristics of the transducer, the transfer matrix method is adopted, in which the transducer is radially divided into n equal-width annular elements connected mechanically in series. Based on Mindlin plate theory, the radial displacement at the mid-plane and electrical transfer parameters are introduced. Combined with boundary conditions, the analytical method is utilized to derive the resonance frequency equations for both bending vibration and coupled radial-bending vibration of the transducer, as well as the analytical expression for its input impedance. The proposed theoretical model accounts for both the radial-bending coupling effect and the electrical parameters of the transducer, and is capable of accurately and efficiently calculating the resonance frequencies and impedance curves for both bending and coupled radial-bending vibrations of unimorph transducers with arbitrary thickness and diameter. To verify the validity of this theoretical model, the finite element method was employed to numerically simulate the vibration modes and impedance frequency response of the transducer. The relative errors of the first four vibration modes and their resonance frequencies were compared under different values of the thickness-to-diameter ratio (h/R). Additionally, a prototype transducer was fabricated, and its impedance characteristics and vibration modes were experimentally measured. The results indicate that the resonance frequencies obtained from theoretical calculations agree well with the results of numerical simulations and experimental measurements. This theoretical model provides a rapid analysis method for the optimization and design of the unimorph transducers and offers theoretical support for practical engineering applications.