The present work concerns with the effects of the permeability of the wall through an overlapping constriction in an artery assuming that the flowing blood is represented by a two-fluid model. The expressions for the blood flow characteristics, the impedance, the wall shear stress distribution in the stenotic region and the shearing stress at the stenosis throat have been derived. Results for the effects of permeability as well as of the peripheral layer on these blood flow characteristics are shown graphically and discussed briefly.