The propagation of acoustic waves on the cylindrical boundary between the core and cladding materials of a clad rod waveguide is described. Typically, axisymmetric torsional, axisymmetric radial‐longitudinal, and core‐guided shear modes may propagate within a rod of cylindrical cross section if the velocity of plane shear waves in the cladding material exceeds the velocity in the material of the core [R. N. Thurston, J. Acoust. Soc. Am.64, 1 (1978)]. If instead the elastic constants of the core and cladding materials of the rod are reversed so the material with the slower shear wave speed is on the outside, no modes are supported within the core but an interface wave can exist on the core‐cladding boundary. In this paper the transmission properties of an all glass clad rod with a suitable core‐cladding elastic constant relationship to support non‐attenuating interface waves are discussed. The resulting improved freedom from spurious responses allowed by this single mode operation is discussed. [Work supported by NASA.]