A “curvilinear wedge” finite‐element has been developed which is broadly applicable to the family of transducers variously classified as “flextionsional” [G. A. Brigham and L. H. Royster, J. Acoust. Soc. Am.46, 92(A) (1969)]. The essential aspects of the direct development of the finite element in cylindrical coordinates are presented, with emphasis on advantages over elements employing polynomial mappings. The resolution of the problem of infinite energy density at the coordinate singularity is effected under conditions sufficiently general for the solution of problems arising in the mathematical modeling of flextensional transducers. Results for the short‐circuited normal modes are presented for Class II, Class IV, and Class V configurations and compared to experimental and other analytical results for these transducers. Good agreement of the predicted spectra with reported experimental data is found. It is demonstrated that constraints in interface compatibility specifications in multicomponent models may produce large errors and involve generally untenable assumptions.