Abstract.A mathematical analysis on blood flowing through a catheterized stenosed artery is carried out using Mathematica, where a package has been developed to solve a Newtonian model of blood flow. This package can be extended to solve and simulate other fluid models and boundary conditions. Investigation centres on the effect of inserting a catheter, which is a tube, used amongst others in patients who are bedridden and whose blood pressure needs to be measured and monitored continuously. Inserting a catheter in an artery is expected to alter some characteristics of blood flow such as velocity, the wall shear stress and the streamlines. The present model considers the catheter and the artery to be in an eccentric position which is more realistic physically compared to the usual model which considers concentric position. The governing equations are solved analytically by a perturbation method. A problem to be tackled is the intimidating and horrendous mathematics involved in the solution procedure. An algorithm to circumvent this difficulty ought to be developed and it is conjectured that Mathematica based algorithm would be able alleviate such problem. Results show that the eccentricity causes the axial velocity and wall shear stress to increase. There is also a trapping bolus which occurs in the region between the wall of stenosis and the wall of catheter for small values of eccentricity parameter.