The circulatory system consists of a pump (the heart) and an extensive, highly branching system of tubes (blood vessels) containing a fluid (blood) with specialized capabilities for the transport of oxygen, nutrients, many other substances and heat. The rates of blood flow through the blood vessels depend on many physical factors, including the diameters, lengths and other geometric features of the vessels, their mechanical properties, the structures of networks that they form, the pressure generated by the heart to drive the flow, and the rheological properties of the blood. All of these factors are themselves subject to variation according to a number of short-term and long-term biological control mechanisms. In order to understand this system, it is helpful to start by considering the mechanics of fluid flow through a single tube with a uniform cylindrical cross-section. Under appropriate conditions, the relationship between driving pressure and flow rate can be described by the equation generally known as Poiseuille's law. In this chapter, a derivation of this equation is presented, and its restrictions and limitations are discussed. This provides a basis for consideration of a range of more complex fluid dynamical phenomena occurring in the circulatory system. More detailed discussions of many of the topics mentioned here can be found in the several books [1-5].