Blood flow is more viscous than water, arteriole wall is elastic, and flow is unsteady. In this study, numerical simulation of blood flow in the Carotid artery is carried out for a 54 years old person. The geometry used in this simulation is the actual geometry of the processing computed tomography scan including 34 millimeters of common Carotid artery and 15 millimeters of internal and external Carotid arterioles at the right side of the head. Radius of the common Carotid artery at the inlet is 3 millimeters, and at the outlet of the internal Carotid and external Carotid are 2 and 1.5 millimeters, respectively. Wall thickness in all arterioles are assumed 0.5 millimeters. The ANSYS-CFX software is used to simulate the blood flow with elastic and rigid walls hypothesis. The whole domain grid includes 86971 cells. The time step was set as 0.016 second. Two Newtonian and four non-Newtonian models are used for the rheeology of the blood. Boundary condition at the inlet of the Carotid artery is defined as the mass flow and the mass flow is given for one pulse of heart beep. The displacement of input and output boundary condition is set to zero and the velocity at the inlet of common carotid is given as uniform. Artery densities were assumed 1060 and 1200 kilogram per cubic meter. Hemodynamic characteristics such as fluid velocity, wall shear stress, wall displacement, and fluid pressure at different sections have been estimated. It is shown that the velocity near the wall in the elastic wall models is more than one obtained in the model with rigid walls. Maximum velocity in the Carotid artery occurs in Carreau-Yasuda's method. It is observed that there is an area with largest displacement at the middle of common Carotid artery. It is concluded that the aneurysm disease in such area is most likely to happen and atherosclerosis has least occurrence. The results show that there is not any separation zone in the internal Carotid artery, because the intersection of the internal and external Carotid arterioles has low angle (about 37 degrees). The velocity gradient and the wall shear stress at the exterior wall of the external Carotid artery are low where the conditions for the development of atherosclerosis commence. The wall shear stress increases at the intersection of the internal and external Carotid arterioles. In this region, the occurrence of aneurysm is more likely to happen than any other region. It is shown that Carreau's and Carreau-Yasuda's rhelogical models better estimate the characteristics of the blood flow than model with Cross rhelogical model. The total pressure (static pressure plus dynamic pressure) in the internal Carotid is almost constant. It is concluded that by analyzing the result of an actual sample of Carotid artery, the cardiovascular disease can be predicted.