A model consisting of two elastic beams separated by hinged rods is used to analyze the axially nonuniform collapse of an elastic tube extending into a pressure vessel. The conditions for which the tube will close are determined experimentally. A self-excited oscillation of the deformation is observed over a range of a factor of 10 in reservoir pressure. The frequency of the oscillation is from 10–100 Hz when water is the fluid flowing out of thin-walled Penrose drainage tubing and approximately 2000 Hz when air is the fluid. A second model is analyzed to describe the important features of the oscillation.