Flow-induced vibration in a collapsible tube is relevant to many biomedical applications including the human respiratory system. This paper presents a linear analysis of the coupling between Poiseuille #ow and a tensioned membrane of "nite length using an eigenvalue approach. The undisturbed state of the channel #ow is perfectly parallel. To some extent, this con"guration bridges the gap between two types of theoretical models: one for the travellingwave #utter in an in"nite, #exible channel, and the other for the self-induced oscillation of a collapsing section of a Starling-resistor tube. In our study, we focus on the parameter range where the wall-to-#uid mass ratio is high (100), and the Reynolds number based on the maximum #ow velocity in the channel is moderately high (200). Eigenmodes representing both static divergence and #utter are found. Particular attention is paid to the energetics of #utter modes. It is shown that energy transfer from the #ow to the membrane occurs as a result of unstable, downstream-travelling waves, while the upstream-travelling waves are stable and release most of the transferred energy back to the #ow. Coupling between di!erent in vacuo modes o!ers another view of the origin of energy transfer. In addition, an energy conservation analysis similar to the one used in aeroacoustics is carried out. It is shown that terms directly proportional to #uid viscosity contribute most to the production of #uctuation energy, leading to a special type of dynamic instability which resembles both Tollmien}Schlichting instability in the sense that the #uid viscosity destabilises, and traditional travelling wave #utter since the structural damping plays the role of stabilising. E!ects of the membrane mass, length and structural damping are also studied. The characteristics of the membrane #utter are found to depend crucially on the upstream and downstream boundary conditions.