We study the flow of a Newtonian fluid through a vessel provided with valves ensuring a unidirectional motion and whose walls are animated by periodic peristaltic waves. The ultimate target is to describe the phenomenon of vasomotion, consisting in periodic oscillations of blood vessels walls which is particularly important for the blood flow in arterioles and veins. We formulate a mathematical model based on approximations of the flow equations due to the smallness of the radius-to-length ratio. Concerning venules, the model reproduces the periodic pressure pulses that have been experimentally detected in bat wing venules.
