In the present work, the Anaerobic Digestion Model No. 1 (ADM1) for computer simulation of anaerobic processes was extended to the processes of sulfate reduction. The upgrade maintained the structure of ADM1 and included additional blocks describing sulfate-reducing processes (multiple reaction stoichiometry, microbial growth kinetics, conventional material balances for ideally mixed reactor, liquid-gas interactions, and liquid-phase equilibrium chemistry). The extended model was applied to describe a long-term experiment on sulfate reduction in a volatile fatty acid-fed upflow anaerobic sludge bed reactor and was generally able to predict the outcome of competition among acetogenic bacteria, methanogenic archaea, and sulfate-reducing bacteria for these substrates. The computer simulations also showed that when the upward liquid velocity in the reactor exceeds 1 m / d, the structure of the sludge becomes essential owing to bacterial detachment.