Though numerous models have been developed to describe the growth of microbial cell cultures, far fewer models are available to describe the growth of hairy root cultures. Here a population balance model is proposed to simulate the growth of hairy roots. The model accounts for the increase in biomass due to elongation of a branch by cell division as well as the formation of new branches. The model incorporates the fact that although the likelihood of the formation of a new lateral branch is a maximum at a specific age of the parent branch, lateral branches can form over a distribution of ages of the parent branch. Model parameters are estimated using the genetic algorithm based on experimental data for batch and continuous bioreactors. The model proposed here may provide a better understanding of the increase in biomass of hairy root cultures.