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A review of the modeling of biogas production from anaerobic digesters is first conducted. A three-dimensional numerical simulation model that predicts biogas production from a plug-flow anaerobic digester is developed. The model is based on the principles of continuity, energy, and species transport. A first-order kinetic model is used to predict the chemical reactions and BOD (Biological Oxygen Demand) in the digestion process. A userdefined function for computing the chemical source terms of the finite rate model is developed. The anaerobic digestion and simulation are conducted using Fluent 6.1 to predict the temperature profile and concentration distribution in the digester. Model predictions are validated against experimentally measured biogas production data obtained from the literature. The results agree within 5%.