A Mathematical model for the pulsatile blood flow through stenosed artery with the effect of body acceleration and slip velocity is proposed. Blood has been represented by casson fluid equation. Analytic expression for velocity, flow rate, wall shear stress and effective viscosity is derived. Flow variables with the change of parameters are represented graphically. The effect of pulsatility, stenosis, body acceleration, slip velocity, yield stress has been investigated. It is found that yield stress of the fluid and body acceleration highly influenced the velocity of the fluid, shear stress, flow rate in a stenosed artery. High blood viscosity is dangerous in the cardiovascular disorders; the present model may be used as a tool for reducing the blood viscosity by using slip velocity at the constricted wall.