Resumo: We present some problems raised by the simulation of blood flows in large arteries. The main issue that we adress is a fluid structure interaction problem in a portion of artery: we propose an approach to couple the original 3D equations with a convenient 1D model. This multiscale strategy allows for a dramatic reduction of the computational complexity and is suitable for ``absorbing'' outgoing pressure waves. We also present some new works on the Saint-Venant equations -- also known as the "shallow waters equations" -- and we explain how these results could improve the 1D models for blood flows.