In this paper, the propagation of harmonic waves with an arbitrary number of circumferential nodes in an infinitely long two-layered composite circular elastic rod is investigated. The composite rod is made of a circular solid rod encased by a circular shell having different material properties. The frequency equation derived on the basis of the three-dimensional linear isotropic elastic theory is presented. The reduction of this equation to the frequency equations for some special problems, such as longitudinal wave propagations, torsional wave propagations, flexural wave propagations, axial-shear vibrations, and plane-strain vibrations is discussed. Simplified equations for phase velocities of longitudinal and torsional waves at very long wavelength are obtained. Numerical results, in terms of frequency and real wavenumber, are given for a composite rod made of a soft core with a stiff casing. © 1971, Acoustical Society of America. All rights reserved.