The design of efficient low-frequency flextensional sonar transducers is a present challenge which is made difficult by a partial lack of general accurate mathematical models. Thus the application of the finite-element method to this problem is a promising approach which has been worked recently. To test the ability of the finite-element code atila [Decarpigny et al., J. Acoust. Soc. Am. 78, 1499–1507 (1985)] to predict the in-air and in-water dynamic behavior of such structures, an axisymmetrical thin-shell transducer was built, and its acoustical behavior was experimentally and numerically analyzed. This paper first presents the modal analysis of this projector, using different finite-element meshes as well as a mixed finite-element–plane-wave model and the comparison of numerical displacement field values to holographic measurements. Second, it describes an in-water harmonic analysis in which the model of the infinite fluid domain is reduced to a portion of the acoustic nearfield, limited by a spherical boundary upon which special damping finite elements are attached. All farfield quantities are then calculated using an efficient extrapolation algorithm [R. Bossut and J. N. Decarpigny, J. Acoust. Soc. Am. 86, 1234–1244 (1989)]. Finally, measured transmitting voltage response and directivity patterns are compared to the finite-element predicted values. The comparison proves the ability of the finite-element approach of provide detailed and accurate insights in the behavior of transducers working with shell vibrations.