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Peristaltic pumping has been the object of scientific and engineering research in recent years. The phenomenon of peristaltic is defined as expansion and contraction of an extensible tube in a fluid generate progressive waves which propagate along the length of the tube, mixing and transporting the fluid in the direction of wave propagation. The study of mechanism of peristaltic in both mechanical and physiological situations has recently become the object of scientific research. The book have two problems in the first problem we discussed slip effect of peristaltic transport of MHD fluid through a porous medium with variable viscosity. We have created the analytical solution with sequential form in terms of viscosity coefficient in the case of the hydrodynamic fluid and magnetohydrodynamic fluid,in the second problem we discussed effects of rotation and MHD on the nonlinear peristaltic flow of a Jeffery fluid in an asymmetric channel through a porous medium and we show the effect of different parameters that control the equations of motion through graphs in both problems.This book will benefit to students, Researchers of M.Sc and Ph.D in Mathematics,Physics and Engineering.