A mathematical model has been developed for the studying of pulsatile flow of blood through a stenosed artery with periodic body acceleration. Herschel – Bulkley fluid has been taken to represent the non-Newtonian character of blood. Perturbation method is used to solve the resulting system of non-linear partial differential equation with appropriate boundary condition to analyze the flow. Analytical expressions are obtained for axial velocity, volumetric flow rate and wall shear stress. Their variations with different flow parameters are plotted in figures. It has been observed that the axial velocity increases as body acceleration increases but the volumetric flow rate increases with the increase of body acceleration with time.