Non-Newtonian fluids are described by a broad classification system interms of the complexities that arise in describing the flow properties. A simple classification is also discussed by many Mathematicians depending on whether the fluids has an elastic response to the applied stress there are two general categories viz., Visco-inelastic (or purely viscous) and Visco-elastic.It is known that most of the physiological fluids behave like Non-Newtonian fluids. Since experimental evidences on blood flow indicate that under certain conditions the flow may have strong deviations from Newtonian flow behaviour. It is also known that one of the major mechanism, for fluid transport in many biological system is the mechanism of contraction and expansion imposed on flexible tubes, which we refer to as Peristalsis. This peristalsis is involved in vasomotion of blood through blood vessels, urine transportation from kidney to bladder through the ureter, movement of chime in the gastro – intestinal tract, transport of spermatozoa in the ductus efferents of the male reproductive system and movement of ovem in the fallopian tubes.