Abstarct: : Many of the cardiovascular diseases that danger life and health of human, are related to conditions of the blood flow inside vessels. Over the past few decades, investigation of the blood flow through the arteries and event of stenosis in them have been the focus of many researchers. The arteries stenosis causing changes in mechanical and dynamics parameters of blood flow in the arteries, and leading to cardiovascular diseases such as atherosclerosis and increased blood concentration. To simulate blood flow through the arteries with stenosis and investigation of influencing parameters can be used to study the effects of these diseases.As well as a better understanding of cardiovascular disease, by finding new ways to improve the treatment of diseases associated. The main purpose of this research, analyze and evaluate influence of different parameters and cramps (25, 50 and 75 percent) for the pulsatile flow of blood into the viscoelastic arteries. The innovation of this study is modeling of pulsatile flow of blood non-Newtonian fluid and its interaction with viscoelastic arterial to study the atherosclerosis and the increasing blood concentration diseases. In this research, profiles of velocity and pressure, redial displacement and shear stress of arterial wall, regions of the vortices are investigated. Also the results of the non-Newtonian fluid flow of blood inside the viscoelastic and elastic arteries have been compared with each other. Then, the effects of the diseases called atherosclerosis (arterial elastic modulus changes) and the increasing blood viscosity (n index changes in Carreau-Yasuda model) on the axial velocity changes, pressure distribution, shear stress and radial displacement of arterial wall are studied. The increasing of stenosis percentage for the viscoelastic artery compared with elastic artery, maximum values of velocity profile and redial displacement of artery wall to the 2% increase and 22% decrease respectively. Progression of atherosclerosis increases the elastic modulus and causes 64 percent reduction in radial displacement of artery wall and 11 and 12 percent increase in the velocity and pressure magnitudes of blood flow. Increasing value of power index lead to growth of maximum value of shear stresses on artery wall for stenosis region. So the increasing of blood viscosity lead to high pressure of blood flow (at a rate of 74.2 percent), growth of the radial displacement of the viscoelastic arterial wall (at a rate of 65.64 percent) and a decrease in the velocity magnitude of flow (at a rate of 50.2 percent) in the region before stenosis.