Atherosclerosis is the most common cause of heart diseases. By reason of fatality of the heart diseases, it is necessary to understand this phenomenon well. In order to have a better comprehension on the blood flow, one of the easiest way is by developing a numerical simulation. It this thesis, the numerical simulation is built upon the Smoothed Particle Hydrodynamics (SPH) Method. The behavior of the blood flow is observed by applying SPH to the Navier-Stokes Equations. There are some cases considered: the normal vessels in which no plaque is existing, and the narrowed vessels, where plaques may exists in various thickness. The numerical results show that the particles’ velocities are increasing when they are flowing on the narrowed vessels. It is also shown that the vessel wall near the plaque suffers from a great pressure. However, there are some empty space on the right side of the plaque, which does not fit the actual condition in the blood vessel. A new model of boundary equation is introduced, involving the hyperbolic tangent function to modify the thickness of the plaque. In addition, an inlet and outlet domain extension is applied so that the disturbance of the plaque does not affecting the behavior of the particle entering the visual domain. This case yields better results: no empty spaces, the behavior of particles which enter the visual domain does not affected by the plaque, and the conservation of mass is satisfied.