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