During the last decade, several types of compact piezoceramic-driven barrel-stave flextensional transducers were researched and developed at the Defence Research Establishment Atlantic (DREA) for low-frequency high-power sonar applications. These transducers were designed to operate at the fundamental flexural resonance where they radiate sound efficiently and omnidirectionally. However, an important limitation common to almost all underwater flextensional transducers is that they require some form of depth compensation for operation at water depths exceeding a few hundred meters. One technique that may eliminate the need for depth compensation (and the associated design complications) for the barrel-stave flextensional transducer is to free flood the cavity inside the cylindrical ring-stack piezoceramic driver with the surrounding acoustic fluid medium and exploit the resulting Helmholtz resonances. To examine the feasibility of such a design approach, the flexural and Helmholtz resonances of a theoretical barrel-stave flextensional transducer with a free-flooded driver have been studied using finite-element techniques, and the results are presented in this paper. In addition, it is shown that the Helmholtz resonance in an experimental transducer does exist and may be practical.