In the present study the problem of a two-layered model for an unsteady and pulsatile flow of blood through a stenosed artery is numerically simulated. The model consists of a core layer of suspension of erythrocytes and a peripheral plasma layer. The core is assumed to be represented using a micropolar fluid and the plasma layer using a Newtonian fluid. The artery is considered to be elastic and the geometry of the stenosis is taken as time-dependent, however a comparison has been made with the rigid ones. The shape of the stenosis in the arterial lumen is chosen to be axially non-symmetric but radially symmetric in order to improve resemblance to the in-vivo situations. By applying a suitable coordinate transformation, the stenosed artery turns into a rectangular and rigid artery. The Navier-Stokes equations of motion of the blood flow, subjected to a pulsatile pressure gradient are solved numerically using the finite difference scheme. Dynamical characteristics of the blood flow such as the velocity profile, the volumetric flow rate and the resistance to flow are obtained and the effects of the wall motion and the severity of the stenosis on these flow characteristics are discussed. The results are found to be in good agreement with the available analytical results.