The continuum theory provides a framework in which the growth of a plant root as a dynamic process involving interactions among transport of water and solute, cell division, and the subsequent cell elongation can be described. A plant root is modeled as a one-dimensional, multi-phase, mathematical continuum. The network of cell walls constitute the solid phase of the system. The symplast and the apoplast pathways reside in this network of cell walls. Water and carbohydrates move in opposite directions through the apoplast and symplast pathways within the deforming network of cell walls. The division and elongation of cells depends on the mechanical stress imposed on the cell walls, the rate of metabolic stress relaxation process, and the physical properties of the cell walls. The model consists of five systems of differential equations. The kinematic equations are derived which allow, specifically, the different roles of cell division and elongation in root growth to be considered. These provide the reference system of the model. Equations of water transport in the coupled system of apoplast and symplast pathways are derived from considerations of theories of transport in the porous media and the cellular and membrane properties of the plant root. Equations of solute transport are derived by considering, specifically, the mechanisms involved in solute transport both at the membranes separating individual cells and within the cytoplasm. The rate of cell elongation is described as a function of the mechanical stress in the cell walls, the viscoelastic properties of the cell walls, and a metabolically controlled strain energy relaxation process. Growth in the meristem is modeled as the result of continuous cell elongation and division. The equations of water and solute transport, cell elongation, and meristem growth are solved simultaneously under the reference system provided by the kinematic theory. The model is used to examine the effects of soil water stress, soil resistance to root penetration, and temperature, as well as the carbohydrate supply from the upper part of the plant on the dynamic process of root elongation. The close correspondence between the material coordinate system and the underlying cellular structure of the root allows the comparison between the continuum theory and the results of cell growth studies. Agreement of the model predictions of the pattern of growth along the root axis, as well as the effects of temperature and soil water stress on root growth, with the experimental measurements reported in the literature provides the justification for the theories. / Graduation date: 1991