Due to the inherent complexity of flexural vibration systems, a comprehensive yet concise equivalent circuit analytical model for sandwich-type piezoelectric flexural vibration transducers has not been fully established. The equivalent circuit method, valued for its simplicity, intuitiveness, and clear physical significance, has become a crucial theoretical tool for the design and analysis of ultrasonic vibration systems. To refine the theoretical design model for sandwich-type piezoelectric flexural vibration transducers, an M-θ distributed parameter equivalent circuit model for transducers with a circular cross-section is developed based on Timoshenko beam theory and the electromechanical analogy principle. From the equivalent circuit model of the sandwich-type flexural vibration piezoelectric transducer, the input impedance expression, resonance frequency equations, and the effective electromechanical coupling coefficient are derived. To validate the accuracy of the theoretical model, two sandwich-type piezoelectric flexural vibration transducers operating in the first-order and second-order flexural vibration modes, respectively, are designed based on calculations from the equivalent circuit model and finite element simulation results. Two corresponding experimental prototypes are fabricated. The measured resonance frequencies and flexural vibration characteristics of the transducers are consistent with the results from both the equivalent circuit theory and finite element simulations. This study provides a precise, concise design theory and experimental data to support the engineering design and structural optimization of circular cross-section sandwich-type flexural vibration transducers.