The effects of an overlapping stenosis on blood flow characteristics in an artery have been investigated. To account for the presence of red cells, blood has been represented by a macroscopic two-phase model (i.e., a suspension of erythrocytes in plasma). The coupled differential equations describing the flow of fluid (plasma) and the particle (red cell) phases have been solved and the expressions for the flow characteristics, namely, the impedance, the wall shear stress, the shear stress at the stenosis throats and the shear stress at the critical height of the stenosis have been derived. It is shown that the impedance increases with the hematocrit as well as with the stenosis size. The shear stress at the two stenosis throats assumes the same magnitude. The shear stress at the stenosis critical height assumes significantly lower magnitude than its corresponding value at the throats. With respect to any given parameter, the nature of the variations of shear stresses at the throats and at the critical height of the stenosis is same as the flow resistance.