A precise model has been developed for studying the influence of metallic nanoparticles on blood flow through catheterized tapered elastic arteries with radially varying magnetic field. The model is solved under the mild stenosis approximation by considering blood as viscous fluid. The influence of different flow parameters associated with this problem such as Hartmann number, nanoparticle volume fraction, Grashof number and heat source or sink parameter is analyzed by plotting the graphs of the wall shear stress, resistance impedance to blood flow and stream lines. The influence of the radially varying magnetic field on resistance impedance to flow is analyzed and it is observed that the significantly strong magnetic force tends to increase in resistance.