In this book, the physiological aspects of the regulation of an arterial bloodstream are mentioned. A review of the existing approaches to make the calculations of a stream of blood in elastic blood vessels is examined. It is shown that available methods of calculation of a current of a fluid in the elastic pipelines, based on the standard hydrodynamical equations, cannot adequately describe movement of blood in elastic blood vessels. Ways of modelling pulse waves, as essentially nonlinear effects are also submitted.