Blood vessels, lung airways and many other vessels carrying fluids around the body are flexible. In some instances, fluid-structure interactions can lead to vigorous instabilities, manifested for example as wheezing of airways. I will discuss efforts to understand the mechanism of these instabilities through the use of simplified theoretical models, and then describe recent progress (in collaboration with Matthias Heil) in developing a rational asymptotic model, validated by numerical simulation, of high-frequency self-excited oscillations in a 2D finite-length channel, one wall of which contains a section of membrane. The model demonstrates that this class of oscillation arises as a global mode of the system, in which the rate at which energy is extracted from the mean flow by spatially asymmetric normal modes exceeds the rate of viscous dissipation.