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A mathematical study for two-phase unsteady pulsatile flow of blood through a vessel in the presence of body acceleration is presented in this paper. The blood in the core region is modeled as a non-Newtonian fluid while in the peripheral region it is described as a Newtonian fluid. The effects of body acceleration are also taken into account in this study. The continuity and momentum equations are used to model the proposed problem in terms of a nonlinear partial differential equation. This equation along with initial and boundary conditions is made dimensionless and then solved numerically using finite difference method. The behavior of various flow quantitates is analyzed through a parametric study.