A mathematical model of bacterial leaching reactors is presented. The model incorporates the population (number) balance approach for the modelling of particulate leaching, the balance for the bacterial cell number, which includes populations of bacteria on the mineral surface and in solution, and material balances describing solution reactants and products. The effects of particle-size distribution, particle kinetics, and the residence-time distribution are accounted for in the population balance. The bacterial balances account for the growth of bacteria in solution and on the mineral surface, and for the attachment to and detachment from the mineral surface. The model is solved for the case of batch leaching and for the case of continuous leaching. The batch model is shown to be a good description of batch leaching. Parameters obtained from batch data for the leaching of a pyritic ore are used to predict the performance of a continuous pilot plant. The model predicts results which compare very favourably with data from the continuous pilot plant.