Harmonic waves propagating in a fluid-loaded, composite circular cylinder are investigated. The solid in this case is composed of perfectly bonded, isotropic, linearly elastic, cylindrical layers stacked radially to form a laminated cylinder. The surface impedance of the laminated shell is calculated using a recursive invariant-imbedding algorithm. This algorithm is numerically stable for a wide range of frequencies and circumferential mode numbers. Particular attention is given to the study of subsonic interface waves which propagate unattenuated along a fluid-solid interface. Results are presented which show the effects of layering and curvature on the dispersion spectrum of the subsonic interface waves.