The non-linear blood flow under the influence of periodic body acceleration through a generalized multiple stenosed artery is investigated with the help of numerical simulation. The arterial segment is simulated by a cylindrical tube filled with a viscous incompressible Newtonian fluid described by the Navier-Stokes equation. The non-linear equation is solved numerically using finite difference with the proper boundary conditions and pressure gradient that arise from the heart. The effect of

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... nolds number is also discussed. Results are shown in comparison with the existing models. Mathematics Subject Classification Introduction Nowadays the investigation of blood flow analysis in a constricted stenosed artery is very important in the medical domain because of the fact that many of the diseases such as heart attacks and strokes are related to blood flow and also the physical characteristics of the vessel wall. At present the leading causes of the death in the world are due to heart diseases such as atherosclerosis. Atherosclerosis occurs where the arteries become narrowed and hardened due to an excessive build up of plaque inside the artery wall. The formation of plaque disrupts the flow of blood around the body and leads to different cardiovascular diseases. Atherosclerosis involves an accumulation of low-density lipoprotein in the wall of large arteries, typically where the wall shear rate is low and oscillatory [1] . When the cells do not get the sufficient oxygen due the reduced of flow rate in the artery, then it may produce ischemia, which is typically used as an indicator for surgical intervention such as angioplasty and bypass operations [1, 2] . Modeling of blood flow through arterial multiple stenosis is very challenging. Numerous experimental and computational methods have used to quantify the velocity and wall shear stress of blood flow in human