Steady flow of blood through catheterized arteries is studied by assuming the blood as a two-fluid model with the suspension of all the erythrocytes in the core region as a non-Newtonian fluid and the plasma in the peripheral layer as a Newtonian fluid. The non-Newtonian fluid in the core region of the artery is modeled as (i) Casson fluid and (ii) Herschel-Bulkley fluid. The expressions for the shear stress, velocity, flow rate, wall shear stress and flow resistance, obtained by Sankar and Lee (2008a, 2008b) for the two-fluid Casson model and two-fluid Herschel-Bulkley model are used to get the data for comparison. It is noticed that the plug flow velocity, velocity distribution and flow rate for the two-fluid H-B model are considerably higher than that of the two-fluid Casson model for a given set of values of the parameters. Further, it is found that the resistance to flow is significantly lower for the two-fluid H-B model than that of the two-fluid Casson model. Thus, the two-fluid H-B model is more useful than the two-fluid Casson model to analyze the blood flow through catheterized arteries.