Genetically transformed, "Hairy roots" once developed can serve as a stable parent culture for in vitro production of plant secondary metabolites. However, the major bottleneck in the commercial exploitation of hairy roots remains its successful scale-up due to oxygen transfer limitation in three-dimensionally growing hairy root mass. Mass transfer resistances near the gas-liquid and liquid-solid boundary layer affect the oxygen delivery to the growing hairy roots. In addition, the diffusional mass transfer limitation due to increasing size of the root ball (matrix) with growth also plays a limiting role in the oxygen transfer rate. In the present study, a mathematical model is developed which describes the oxygen transfer kinetics in the growing Azadirachta indica hairy root matrix as a case study for offline simulation of process control strategies ensuring non-limiting concentrations of oxygen in the medium throughout the hairy root cultivation period. The unstructured model simulates the effect of oxygen transfer limitation in terms of efficiency factor (eta) on specific growth rate (mu) of the hairy root biomass. The model is able to predict effectively the onset of oxygen transfer limitation in the inner core of the growing hairy root matrix such that the bulk oxygen concentration can be increased so as to prevent the subsequent inhibition in growth of the hairy root biomass due to oxygen transfer (diffusional) limitation.