This paper derives theoretical solutions for three radially layered piezoceramic/epoxy cylindrical composite transducers, which are composed of a solid epoxy disk, two axially polarized piezoceramic rings, and two epoxy rings. Two piezoceramic rings are the functional components, which can actuate and adjust the composite's performance. According to different functions, three typical transducers are developed. The first one involves both of the two piezoceramic rings acting as actuating elements with parallel connections electrically. The other two involve only one piezoceramic ring as an actuating element, while the other ring that is connected to a resistor acts as a sensing element to adjust the electromechanical characteristics. Based on the plane stress assumption, theoretical solutions of these three transducers in radial vibration are derived, and performance differences of their electromechanical characteristics are analyzed and discussed. Furthermore, the solutions are validated by comparing with the ANSYS simulation results and the experimental data. The simulated and the measured first resonance and antiresonance frequencies are in a good agreement with the theoretical results, which validates the accuracy of the directed solution. This paper contributes to a comprehensive understanding of the proposed cylindrical composite's electromechanical performance, which is helpful for further application in underwater sound and ultrasonic fields.