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The vibroacoustic behavior of an infinitely long cylindrical shell with periodic lengthwise ribs is studied. The shell motion is described by the Donnell equations, and the lengthwise rib is modeled as an elastic beam whose motion is decomposed into longitudinal and flexural vibrations. Analytical expressions are obtained for the shell motion via a circumferential mode expansion based on the periodicity in the circumferential direction and the Fourier transform in the longitudinal direction. Furthermore, the far-field radiated pressure is obtained via the stationary-phase approach. The shell vibration and sound radiation are analyzed using discrete circumferential wavenumbers. Multi-order flexural Bloch waves exist in the circumferential direction when the cylindrical shell is equipped with periodic lengthwise ribs. The supersonic components of the flexural Bloch waves radiate efficiently and lead to acoustic radiation resonances in the far field.