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 non-linear effects are also submitted.