The motivation for this paper is the need to detect radial fatigue cracks in a shaft/bearing assembly (as shown in Fig. 1), using guided circumferential waves. To do so, wave propagation in a layered cylinder must be understood. In order to accurately detect the crack, the dispersion relationship for guided circumferential waves must be known; this enables the selective generation of specific wave modes that carry the most energy to the interface (and to the crack).