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The study of a hybrid system obtained coupling a methane fuelled gas microturbine (MTG) and a solid oxide fuel cell (SOFC) was performed. The objective of this study is to evaluate the operation conditions as a function of the independent variables of the system, which are the current density and fuel utilization factor. Numerical simulations were carried out in developing a C++ computer code, in order to identify the preferable plant configuration and both the optimal methane flow and the current density. Operation conditions are able to ensure elasticity and the most suitable fuel utilization factor. To confirm the reliability of the models, results of the simulations were compared with reference results found in literature.