Blood as a fluid that human and other living creatures are dependent on has been always considered by scientists and researchers.Any changes in blood pressure and its normal velocity can be a sign of a disease.Whatever significant in blood fluid’s mechanics is Constitutive equations and finding some relations for analysis and description of drag,velocity and periodic blood pressure in vessels.In this paper,by considering available experimental quantities,for blood pressure and velocity in periodic time of a thigh artery of a living dog,at first it is written into Fourier series,then by solving Navier-Stokes equations,a relation for curve drawing of vessel blood pressure with rigid wall is obtained.Likewise in another part of this paper,vessel wall is taken in to consideration that vessel wall is elastic and its pressure and velocity are written into complex Fourier series.In this case,by solving Navier-Stokes equations,some relations for blood velocity,viscous drag on vessel wall and blood pressure are obtained.In this study by noting that vessel diameter is almost is large(3.7 mm),and blood is considered as a Newtonian fluid.Finally,available experimental quantities of pressure with obtained curve of solving Navier-Stokes equations are compared.In blood analysis in rigid vessel,existence of 48% variance in pressure curve systole peak caused vessel blood flow analysis with elastic wall,results in new relations for blood flow description.The Resultant curve is obtained from new relations holding 10% variance in systole peak. Blood as a fluid that human and other living creatures are dependent on has been always considered by scientists and researchers. Any changes in blood pressure and its normal velocity can be a sign of a disease. Whatever significant in blood fluid’s mechanics is Constitutive equations and finding some relations for analysis and description of drag, velocity and periodic blood pressure in vessel. In this paper, by considering available experimental quantities, for blood pressure and velocity in periodic time of a thigh artery of a living dog, at first it is written into Fourier series, then by solving Navier-Stokes equations, a relation for curve drawing of vessel blood pressure with rigid wall is obtained. Leadwise in another part of this paper, vessel wall is taken in to that of that vessel wall is elastic and its pressure and velocity are written into complex Fourier series. In this case, by solving Navier-Stokes equations, some relations for blood velocity, viscous drag on vessel wall and b lood pressure are obtained. In this study by noting that vessel diameter is almost is large (3.7 mm), and blood is considered as a Newtonian fluid. Notally, available experimental quantities of pressure with obtained curve of solving Navier-Stokes equations are compared. In blood analysis in rigid vessel, existence of 48% variance in pressure curve systole peak caused vessel blood flow analysis with elastic wall, results in new relations for blood flow description. The Resultant curve is obtained from new relations holding 10% variance in systole peak .