The nonlinear mechanics of the arterial walls is analyzed as an important example of biological solid mechanics. After the introduction of the necessary background on matrices and tensors, the stresses and strains in the arterial wall are defined. Then, the fundamental concept of the strain energy function and its particular forms used in the vascular mechanics are introduced. The experiments (biaxial stretch and inflation-extension) aimed at the estimation of the wall material properties are discussed. In addition to the properties of the normal arterial wall, the mechanics in vascular diseases are studied. First, the stresses and stiffness in atherosclerotic arteries are analyzed, and then the effects of hypertension are discussed. In the second part of the class, the fluid mechanics of blood is studied, including the velocity profiles and shear stress distribution. The non-Newtonian features of blood rheology are presented as well. In the last part of the class, the cells in the blood circulation are considered with the main focus on the red blood cells. The micropipette experiment to estimate the elastic moduli of the red blood cell wall is studied in detail. The recent studies of the red blood cell circulation under pathological conditions (cancer, malaria) are discussed also. In all sections, the latest results of the computational modeling are used to support the main goals of the course. In addition to the regular (weekly) assignments, the students will be given original journal papers to discuss as a group. Finally, the students will be working on a computational project related to one of the major topics of the course.