Axial growth of plant roots can be modeled as the deformation of a one-dimensional continuum. In this study we present a theory of root elongation that incorporates different roles of cell division in the meristem and axial growth in the elongation region in overall root extension. The meristem is idealized as being located at the root tip, from which material points are produced continuously by cell division. Elongation takes place after material points leave the meristem. Each material point along the root axis is associated with a unique time at which it was produced. The total rate of root growth is the sum of the rate of elongation of all cells present plus the contribution from the meristem. Under steady-state conditions, the rate of elongation of a particular segment of the root is a function of its age only. The theory enables us to compare spatial patterns of steady-state root elongation with distribution of cell sizes along the root axis. The theory is also used to characterize the effects of soil water stress and temperature on root growth. Soil water stress reduces both the rate of meristem production and the subsequent cell elongation, resulting in a shorter elongation region. The effect of temperature is characterized by a temperature-time equivalence effect, leading to an elongation region with its length independent of temperature.