This article explores the theoretical investigation of peristaltic motion of a non-Newtonian fluid accompanied in a horizontal channel with elastic walls. Most of the physiological fluids (blood) behaves like a non-Newtonian fluid. To characterize the fluid flow behavior, Casson fluid model is considered which a yield stress model and it holds good to explain the behavior of blood flow through small diameter conduits at low shear rates. The deformation in the walls of the channel is studied under two aspects, one is peristalsis and another is elasticity. Exact solutions are obtained for velocity and stream function. The size of the trapped food bolus increases with increasing values of yield stress parameter. The theoretical obtained results may be useful in understanding of pathological conditions arising due to change in elasticity and different peristaltic wave forms. © 2020 International Information and Engineering Technology Association.