In the present study, a two–layered model of pulsatile flow of blood through a stenosed elastic artery is numerically examined. The two–fluid model consists of a core layer of a suspension of erythrocytes and peripheral plasma layer. It is assumed that the core and peripheral plasma layer behave as micropolar and Newtonian fluids respectively. The resulting system of nonlinear partial differential equations is numerically solved using the finite difference scheme by exploiting the suitably prescribed conditions. Effects of the tapering angle, wall deformation and severity of the stenosis on flow characteristics are discussed. The present results are compared with literature and found to be in good agreement.