The comprehensive analysis of structure and properties was performed for the blood and blood vessels. This analysis shows that the blood may be considered as a liquid only in large and middle vessels, where a diameter of vessel is much more than a dimension of blood cells and their aggregates. In addition, taking into account the influence of complex internal structure on its mechanical properties, it is necessary to consider it as a non-Newtonian liquid. In this regard, the non-Newtonian liquid with the power connection of the stress tensor with the strain velocity tensor was chosen for mathematical modelling of liquid. The pulsating flow is created by the pulsating nature of the boundary condition for the blood flow at the input cross-section. The vessels are considered as thick-walled cylinders with hyperelastic walls. The interaction between blood and vessel wall is defined by means of semi-slip boundary condition. Computer simulation was performed in software complex ANSYS with the use of the direct conjugating module CFX and the module ANSYS “Multiphysics”. As a result, the pressure and stress wave propagation on the vessel wall was obtained.