In the present study, properties of unsteady blood flow through an stenosed artery is investigated. The study has a tapered artery stenosed and asymmetric elastic walls is considered. The flow of blood is assumed to be incompressible, laminar and fully developed. To consider the effect of suspended particles in the blood, fluid model is used to describe micropolar Eringen. Governing equations are extracted and Mild stenosis approximation is applied to simplify. Also, an suitable converted is applied to momentum equations, initial and boundary conditions, the cosine shape mesh grid to regular mesh grid by utilizing suitable transformation. Non-slip boundary condition equations using finite difference method is solved numerically. To investigate the graphical shapes in the study, the effect of parameters related to flow and tapered angle has been the matter of into rest to investigate the Axial and rotational velocity profiles, the volumetric flow rate, Wall shear stress and the resistance to flow. Characteristics of elastic and non-elastic artery are compared and the results confirm the importance of elastic assumed artery. To confirm the accuracy results, these are compared the results of previous literature.