Hemodynamics is the study of the forces and physicalmechanisms associatedwith blood ?ow in the cardiovascularsystem. Due to the fact that blood is a suspension of ?exible particles in plasma and to the coupling between motion of blood and the vessel wall, necessarily this subject includes both ?uid and solid mechanical processes. Hemodynamic features such as ?ow separation, ?ow recirculation, and low and oscillatory wall shear stress are believed to play important roles in the localization and development of vascular diseases such as atherosclerosis, cerebral aneurysms, post-stenotic dilations and arteriovenous malformations. Therefore, modeling, mathematical analysis and numerical simulation of these processes can ultimately contribute to improved clinical diagnosis and therapeutic planning. However, the circulatory system is extremely complex and so researchers are facedwith the need to formulatethe numericalormathematicalproblemin a form which is su?ciently simple to be tractable, yet maintains enough complexity to be relevant.Forexample, ratherthanmodeling the entirecirculatorysystem,isolated segmentsofthe circulationarestudied,introducingthe needtochooseappropriate in?ow and out?ow boundary conditions and possibly take a multi-scale approach. The blood vessel wall is an inhomogeneous, nonlinear, material capable of growth and remodeling, and blood is a concentrated suspension of deformable cellular elements in plasma. The modeler needs to choose suitable constitutive models for the wall and blood. The diameter of vessels in the circulatory system ranges from the order of centimeters in the larger arteries to microns in the capillaries.