Motivated by the application of a metal-rubber laminate bellows structure to replace a component in a thermoacoustic-stirling engine, the static and dynamic properties of such bellows was investigated. In particular, it is found that the transverse resonance frequencies is a function of the differential pressure. However, unlike the case of an ordinary pipe pressurized pipe configured to carry no axial loads, the transverse resonance frequency, at sufficiently high differential pressures, decreases for both internal and external pressure. In service such a bellows experiences both cases, at acoustic frequencies, and this modulation of the resonance frequency can lead to an interesting instability. Aspects of the dispersion curves for such a structure are discussed. In particular, under some load conditions, this kind of structure can have flexural waves that are predicted to exhibit no dispersion, unlike ordinary plates, and to be able to support propagation at more than one phase speed.