Models of root systems are essential tools to understand how crops access and use soil resources during their development. However, scaling up such models to field scale remains a great challenge. In this paper, we detail a new approach to compute the growth of root systems based on density distribution functions. Growth was modelled as the dynamics of root apical meristems, using Partial Differential Equations. Trajectories of root apical meristems were used to deform root domains, the bounded support of root density functions, and update density distributions at each time increment of the simulation. Our results demonstrate that it is possible to predict the growth of root domains, by including developmentally meaningful parameters such as root elongation rate, gravitropic rate and branching rate. Models of this type are computationally more efficient than state-of-the-art finite volume methods. At a given prediction accuracy, computational time is over 10 times quicker; it allowed deformable models to be used to simulate ensembles of interacting plants. Application to root competition in crop-weed systems is demonstrated. The models presented in this study indicate that similar approaches could be developed to model shoot or whole plant processes with potential applications in crop and ecological modelling. (c) 2012 Elsevier Ltd. All rights reserved.