The present paper is concerned with the effect on the flow characteristics of blood due to presence of an overlapping stenosis in an inserted catheterized artery with permeable wall has been investigated. The expressions for the flow characteristics – the flow rate, the impedance (resistance to flow), the wall shear stress in stenotic region, the shear stress at the stenosis two throats and critical height of the stenosis, has been derived. A significant increase in the magnitude of the flow characteristics occurs with respect to flow parameters and catheter size.