This paper comprises the exact solutions of Non-Newtonian multiphase fluid through peristaltic pumping characteristics in an annulus having complaint walls and applied magnetic field. The mechanics of the geometry are
defined cylindrical due to its large number of utilizations in medicine and biological apparatus. The external cylinder is having sinusoidal waves travelling along its walls. The problem is simplified by some suitable and
valid approximations. The authors have obtained the accurate solutions of the velocities of two phases. The effects of appertaining parameters have been displayed through graphs of velocity for v and particulate phases
and the behavior of curves are manipulated accordingly. It is concluded that applied magnetic field decreases the velocity of both the fluid and the particles flow.