A mathematical model of an acid mine drainage system has been developed for underground mines. The model relates the rate of acid formation to the rate of pollution discharge from the system. The calculational model was developed using a digital computer to simulate an existing mine as the sum of many micro scale mines. The input to the model is a physical and chemical description of the system. Day-to-day simulation requires data on temperature, rainfall, and oxygen concentration at the exposed coal face. The output of the model is estimates of daily acid load and drainage flow. The calculational model was based on a carefully described physical model so that a predictive model can be constructed with little or no experimental data. However, methods for constructing the computational model are given which can use the field data available to increase the reliability.