This book presents an account of theories of flow in porous media which have proved tractable to analysis and computation. In particular, the theories of Darcy, Brinkman, and Forchheimer are presented and analysed in detail. In addition, the theory of voids in an elastic material due to Cowin and Nunziato is discussed. The range of validity of each theory is outlined and the mathematical properties are considered. The questions of structural stability, where the stability of the model itself is under consideration, and spatial stability are investigated. Applications to a variety of problems in porous media are included. This book is intended for graduate students and researchers in the mechanics, physics and engineering fields.