The generation of overtones by finite‐amplitude processes in rigid‐walled cylindrical cavities with large length‐to‐diameter ratios is studied. An extension of the Keck‐Beyer perturbation technique leads to a set of iterative equations valid for standing waves that can be applied to cavities with energy losses occurring at the walls. Necessary features of the theory include assuming one‐dimensional motion, characterizing all absorptive processes by a bulk absorption coefficient, and requiring a boundary‐layer depth much less than the tube diameter. Solutions lead to a steady‐state distribution of harmonics of the fundamental, the relative amplitude of each overtone being inversely proportional to the absorption coefficient characteristic of the relevant normal mode of the cavity. [Work supported in part by the U. S. Office of Naval Research and the U. S. Bureau of Ships.]