In this thesis we study fluid-structure systems modelling the blood flow through<br>human arteries. Our analysis involves \textit{realistic conditions} on the inflow and outflow of the vessel and<br>allows for larger deformations than previous studies. We also investigate equilibrium states (when the system<br>is subjected to a periodic impulse coming from the heart) and the stabilization around this equilibrium after<br>perturbations. This work generalises and extends the theoretical study of a model that has been largely used<br>as a benchmark for numerical schemes in mathematical biology.