In this paper a mathematical model of pulsatile, unsteady and non-Newtonian blood flow through elastic tapered artery with overlapping stenosis is proposed. The blood flow has been assumed to be non-Linear, fully developed, laminar, axisymmetric, two-dimensional. The non-Newtonian model chosen is characterized by Sisko model for discribe the rheology of blood. The artery has been assumed to be elastic and time-dependent stenosis is considered. Due to the blood flow depends on the pumping action of the heart, the blood flow has been assumed pulsate. The stenosed artery change in to a rectangular and rigid artery, using a radial coordinate transformation on the continuity and the nonlinear momentum equations and boundary conditions. The discretization of the continuity and the non-linear momentum equations and boundary conditions are obtained by finite difference scheme. The radial and axial velocity profiles are obtained and the blood flow characteristics such a resistive impedances and volumetric flow rate and the severity of the stenosis are discussed. The volumetric flow rate is minimum in the case of converging tapered arteries and the resistive impedances is maximum in the case of converging tapered arteries by effect of tapering angle.