Hydroelastic systems can be characterized by the simultaneous manifestation of elastic and hydrodynamic instabilities and their interaction. Consideration is given to mutual effects of blood vessel bending, internal and external pressures, action of the compression force and fluid with a set density flowing along the blood vessel. A thin elastic blood vessel is "fixed" on clamped sliding supports. In this case the "supports" do not hinder the flow of fluid travelling inside the blood vessel along its axis. On the supports, the blood vessel bending and rotation angle equal to zero. It is assumed that the elastic blood vessel has thin walls and ideal fluids found in and out of the blood vessel are