In this paper, we present an analytical modeling technique for circularly symmetric piezoelectric transducers. We also present the design of a flat/piston transducer that can generate unique acoustic wave patterns, having both converging and vortexing effects. The converging effect is generated by designing the transducer electrodes in the shapes of circular rings using Fresnel formula and exciting it with an RF signal of resonant frequency. The vortexing effect is achieved by cutting the rings to different sector angles: 90°, 180° and 270°. We use the analytical model to simulate the performance of these transducers.