A velocity‐stress finite‐difference (VS‐FD) model is presented for a cylindrical piezoelectric transducer in a borehole. The borehole may be irregular and the surrounding formation inhomogeneous. The model is two dimensional in that azimuthal symmetry is assumed. The description of the tranducer is a full elasto‐electromagnetic one, including transverse isotropy in the elastic, dielectric, and piezoelectric parameters, and dissipation in the piezoelectric material. The borehole propagation portion of the model is verified by comparison with a standard transform technique. Predictions of the model for a piezoelectric cylinder radiating into a fluid medium are compared to experimental results with excellent agreement. The radiation patterns of a bare transducer near resonance frequencies are found to be anisotropic. Acoustic waveforms in a borehole excited by a finite sized cylindrical transducer are displayed and are quite different from those excited by an ideal point pressure source. The effect of borehole loading upon the impedance of the transducer is shown to be small.