In this research, we present an analytical study of the effect of resistance to flow blood through a narrowed artery for catheterization. Vascular diseases are among the most common diseases in countries of the world that can cause cerebral clots or strokes. Where stenosis is the occurrence of abnormal growth on the artery wall, which causes obstruction, in the movement of blood flow, the current model simulates the study of blood flow, given that the blood is Newtonian, incompressible, and steady, with a viscosity and density constant. It was built mathematically to describe the movement of the physiological fluid that represents blood in a gap between two eccentric tubes, where the inner tube is a solid and unified one that represents the moving catheter. While the other is a tapered cylindrical one that represents the artery with overlapping stenosis, where the insertion of the stenosis leads to a change in the blood characteristics (axial velocity, flux and resistance) .The current results showed that the increase in the axial velocity of the stationary catheter is much higher than that of the fixed one, and that the flow resistance increases with the stenosis of the artery.