The objective of the paper being presented is to develop a comprehensive mathematical model of a bagasse gasification unit integrated with a solid oxide fuel cell, to predict the system performance using the energy and exergy criteria. The model addresses the quasi-equilibrium approach of the gasifier and the electrochemical behavior of a solid oxide fuel cell fed with producer gas. The quasi-equilibrium approach is discussed based on the experimental data from a pilot bubbling gasifier for two biomass sources: sugar cane bagasse and rice husk. The model considers the effect of equilibrium temperature, carbon conversion, heat losses and tar removal in the gasifier and the in situ reforming, water gas shift and hydrogen conversion within cell electrodes. The best results are obtained at 1023 K and a 0.30 of air factor, under these conditions the total exergy efficiency is 35.20% and 58.85% of energy efficiency. After systems integration, the major exergy destruction is found in the gasifier ranging from 75% to 80% of the total loss.