The paper presents a mathematical model able to simulate under dynamic conditions the physical, chemical and biological processes prevailing in a OFMSW and sewage sludge anaerobic digestion system. The proposed model is based on differential mass balance equations for substrates, products and bacterial groups involved in the co-digestion process and includes the biochemical reactions of the substrate conversion and the kinetics of microbial growth and decay. Main peculiarities of the model are the surface based kinetic description of the OFMSW disintegration process and the pH determination, which is based on a nine-order polynomial equation derived by acid-base equilibria. The model can be applied to simulate the co-digestion process for several purposes, such as the evaluation of the optimal process conditions in terms of OFMSW/sewage sludge ratio, temperature, OFMSW particle size, solid mixture retention time, reactor stirring rate, etc. In this paper the methane production of a MWWTP digester has been evaluated to assess the model potential to estimate the potential energy production under different process conditions. In particular, model simulations show the model capability to predict the effect of the amount and particle size of an OFMSW addition in the digester of an existing MWWTP on the co-digestion efficiency and methane production.