  We present a two dimensional model describing the elastic behaviour of the
wall of a curved blood vessel. The wall has a laminate structure consisting of
several anisotropic layers of varying thickness and is assumed to be much
smaller in thickness than the radius of the vessel which itself is allowed to
vary. Our two-dimensional model takes the interaction of the wall with the
surrounding tissue and the blood flow into account and is obtained via a
dimension reduction procedure. The curvature and twist of the vessel axis as
well as the anisotropy of the laminate wall present the main challenges in
applying the dimension reduction procedure so plenty of examples of canonical
shapes of vessels and their walls are supplied with explicit systems of
differential equations at the end.
