The transient analysis of piezoelectric transducers is often performed using finite-element or finite-difference time-domain methods, which efficiently calculate the vibration of the structure but whose numerical dispersion prevents the modeling of waves propagating over large distances. A second analytical or numerical simulation is therefore often required to calculate the pressure field in the propagating medium (typically water) to deduce many important characteristics of the transducer, such as spatial resolutions and side lobe levels. This is why a hybrid algorithm was developed, combining finite- difference and pseudo-spectral methods in the case of 2-D configurations to simulate accurately both the generation of acoustic waves by the piezoelectric transducer and their propagation in the surrounding media using a single model. The algorithm was redefined in this study to take all three dimensions into account and to model single-element transducers, which usually present axisymmetrical geometry. This method was validated through comparison of its results with those of finite-element software, and was used to simulate the behavior of planar and lens-focused transducers. A high-frequency (30 MHz) transducer based on a screen-printed piezoelectric thick film was fabricated and characterized. The numerical results of the hybrid algorithm were found to be in good agreement with the experimental measurements of displacements at the surface of the transducer and of pressure radiated in water in front of the transducer.