Blood is a complex fluid that is primarily composed of red blood cells (RBCs), which occupy (in a healthy human body), about 45% of the blood volume. The descriptions of blood flow properties escape the tradi- tional laws for simple fluids. We introduce the generalized Navier-Stokes equations reformulated to describe the non-Newtonian blood behavior . Being a non standard formulation, we carry out a well posedness analysis, providing an existence result for the evolutionary case. Moreover blood flow interacts mechanically with the vessel wall. A fluid-structure interaction (FSI) model where interactions between the fluid (blood) and structures (the arterial wall and atheromatous plaque) are conducted by an Arbitrary Lagrangian Eulerian (ALE) method in the case of numer- ical simulations. We provide an energy estimate for the coupling and compare the numerical results with those obtained with an equivalent fluid-structure interaction model using a Newtonian fluid and a fixed wall.