In this study,a mathematical model is formulated to examine the blood flow through a cylindrical stenosed blood vessel.The stenosis disease is caused because of the abnormal narrowing of flow in the body.This narrowing causes serious health issues like heart attack and may decrease blood flow in the blood vessel.Mathematical modeling helps us analyze such issues.A mathematical model is considered in this study to explore the blood flow in a stenosis artery and is solved numerically with the finite difference method.The artery is an elastic cylindrical tube containing blood defined as a viscoelastic fluid.A complete parametric analysis has been done for the flow velocity to clarify the applicability of the defined problem.Moreover,the flow characteristics such as the impedance,the wall shear stress in the stenotic region,the shear stresses in the throat of the stenosis and at the critical stenosis height are discussed.The obtained results show that the intensity of the stenosis occurs mostly at the highest narrowing areas compared with all other areas of the vessel,which has a direct impact on the wall shear stress.It is also observed that the resistive impedance and wall shear pressure get the maximum values at the critical height of the stenosis.