The modeling of two-layered blood flow an inserted catheterized artery has been invstigated. The flowing blood is considered to be incompressible, Newtonian with variable blood viscosity. The functional dependence of blood viscosity on haematcroit (percentage of red cells) has been duly accounted for in order to improve resemblance to the real solution. It is noticed that the effective viscosity, flow rate and arterial wall shear stress in particular, in the catheterized site, are significantly altered. Flow characteristics assumes, its lower magnitude in catheterized artery as compared to the uncathetrized artery for any given set of parameter. Numerical results reveal that the effective viscosity in minimal magnitude and consequently the flowrate assumes its maximal magnitude during the artery catheterization at the catheter size approximately fifty percent to that of artery size.