  We exploit a two-dimensional model [7], [6] and [1] describing the elastic
behavior of the wall of a flexible blood vessel which takes interaction with
surrounding muscle tissue and the 3D fluid flow into account. We study time
periodic flows in a cylinder with such compound boundary conditions. The main
result is that solutions of this problem do not depend on the period and they
are nothing else but the time independent Poiseuille flow. Similar solutions of
the Stokes equations for the rigid wall (the no-slip boundary condition) depend
on the period and their profile depends on time.
