The growth of hairy root cultures in bioreactors yields a complex root network and limits nutrient availability to the inner core of the root bed. A kinetic growth model to explain the growth in terms of length of individual primary and their higher order branches has been developed. The external transport of nutrient modeled based on mass transfer rate of limiting nutrient across root surface and internal transport of nutrient modeled based on flow of nutrient from primary to secondary roots. The growth reaction constant during elongation phase, which is function of limiting nutrient concentration found to be in the range of 0.1 to 0.4 d⁻¹ for various species through fitting. The model equations are well fitted with the experimental data with minimum root mean square error for the ratio of radius of primary to secondary root is 1.5, the nutrient to biomass ratio in the range 1.5 to 4.0 and the inter node distance is the range of 0.2 to 0.5 cm. Higher growth coefficients, smaller inter node distances yields large number of tips and higher growth of primary and secondary roots. Higher growth coefficient can be achieved by manipulating nutrient medium concentration and cells reach branching age faster which alters the inter-node distance and branching rate. This model will be a crucial input to estimate packing fraction and local concentration profile in the growing hairy root bed in bioreactors.