Dispersion curves, leakage loss, and displacement profiles obtained from the exact analysis of leaky torsional acoustic modes in infinitely thick cladded rods are presented. Two different structures, in which both the longitudinal and the shear velocities of the core are either larger or smaller than those of the cladding, are considered. Similarities are observed between results obtained and dispersion curves which have been reported previously by other workers. Analytic loss relations are also reported for specific modes at either the low‐ or the high‐frequency limit. Applications for this analysis are discussed.