Blood clotting, or hemostasis, is a vital process in the human body. Bleeding disorders, such as hemophilia, arise when hemostasis occurs on too slow of a timescale or not at all. On the other end of the spectrum, if clotting occurs too rapidly (thrombosis), pathological clots, or thrombi, can form, leading to heart attacks and strokes. Understanding how blood clotting occurs requires knowledge of biophysical and biochemical processes which take place over multiple scales in both time and space. Fluid flow is an integral component of the blood clotting system. Blood flow brings platelets and chemical reactants required for clot growth to a vascular injury site. In addition this flow imposes mechanical stresses that affect the formation and breaking of molecular bonds. In this talk we will discuss how the immersed boundary method can be used as a mathematical modeling framework to study both the fluid structure interactions of platelets moving in a blood vessel and how the platelets bind to the vessel wall in response to injury.