The wavenumber‐frequency structural response of a fluid‐loaded, periodic ring‐supported, circular cylindrical shell is modeled. In the model, the ring supports are assumed to interact with the shell only through normal forces. The TBL pressure fluctuation wavenumber‐frequency spectra models of Corcos [J. Fluid Mech.18, 353–378 (1964)] and Chase [J. Sound Vib.70, 29–67 (1980)] are used in this effort. Sums are taken over wavenumbers to obtain predictions of the average shell response to TBL excitation as a function of frequency. Bands of wavenumbers that control the shell response are identified for different frequencies and shell configurations.