The study of flows through porous medium has been the topic of considerable research activity by both theoretical and experimental investigators for the last one and half centuries. The subject of flows through porous medium assumed importance because of its interesting many applications in the diverse fields of science, engineering and technology. The classical theory of flows through porous media has been extensively reported in several treaties. The studies are initiated in the middle of the nineteenth century by Henry Philibest Graspard Darcy, while investigating the flow of water purification plant in the city Dijon in France. Darcy, based on a series of experiments, formulated an empirical law for the flows through porous medium. The main aim of the book is the study of the flows of Newtonian and non-Newtonian through the porous medium. One general observation in all the situations is that the non-Darcian effect is more predominant in a thin region around the bounding surface. The thickness of the region is of, where K is the permeability coefficient of the medium. At large distance from the boundary the flow will be of Darcian in nature.