First, the concepts from mechanics and thermodynamics are rehearsed for single component mixtures. Next mixture theory is dealt with in a general fashion. The balance laws for mass, momentum, angular momentum. energy and entropy are formulated per component and for the mixture as a whole. The procedure for formulation of constitutive restrictions from objectivity, equipresence and the second law of thermodynamics is clearly outlined and applied to three examples.All three examples are dealt with in finite deformation, as soft biological tissue and cells are imprortant applications. The first example is two-component mixture composed of a porous solid and a liquid. This model can be viewed as a rudimentary model of a biological material or a soil. The constitutive model for the effective stresses is non-linear elastic, while the flow model for the liquid is Darcy's law. Consolidation and capillarity are important features. In the second example, the two-component mixture is extended to a four component mixture, including ions in the liquid. In addition the solid is ionised as well. This model is particularly suitable for cartilage, cartilaginous material and clays. Presently, its applicability to cells and the pericellular evironment is being investigated. The model is able to describe streaming potentials, diffusion potentials, intra-extracellular potential differences, swelling and Donnan osmosis. In the third example blood perfusion is presented. The liquid component is subdivided in a number of liquid compartments (arterial, arteriolar, capillary, venular and venous) which intercommunicate. Blood perfusion is a vital form of convective transport in biology, in those cases where diffusion cannot be sufficient. All of the examples are drawn from the current research themes and are therefore state-of-the art models. Along the chapters the results are related to in vitro and in vivo experiments.