This book presents a unified treatment of the mechanics of mixtures of several constituents within the context of continuum mechanics. After an introduction to the basic theory in the first few chapters, the book deals with a detailed exposition of the mechanics of a mixture of a fluid and an elastic solid, which is either isotropic or anisotropic and is capable of undergoing large deformations. Issues regarding the specification of boundary conditions for mixtures are discussed in detail and several boundary value and initial-boundary value problems are solved. The status of some special theories like those of Darcy and Biot are discussed. Such a study has relevance to several technologically significant problems in geomechanics, biomechanics, diffusion of contaminants and the swelling and absorption of fluids in polymers and polymer composites, to mention a few.