In this paper we present a dynamic model of the heart’s pumping blood. To predict blood flow and pressure applied to the area of blood vessels (arteries - veins - capillaries). The fluid dynamics model is derived from the continuum equation and the Navier-Stokes equations. For an incompressible Newton flow through a network of cylindrical vessels. This paper combined a model of pressure applied to the walls of blood vessels with a (regular - turbulent) flow model of blood, and the viscoelastic deformation of the walls (arteries - veins - capillaries) was studied with different blood density and prediction of the effect of the thickness of the rubber wall on the flow and the resulting pressure on the blood vessels. The results of this study show that the viscous elastic wall of the blood vessels allows more physiological prediction of pressure and vascular deformation, and that blood flow with varying intensity is more in the aorta than in the rest of the vessels, and this is subject to wide dilation.