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In this work we present an extended version ofthe Friedrichs Model (FM), which includes fermions. The standardFM describes the coupling between discrete and continuouscomponents of a boson field. It is an exactly solvable model whichallows for a clear identification of Gamow Resonances. In thisextended version a set of fermion bound states is coupled to theboson field. As a result of the coupling some of the fermionstates become resonant states. The structure of the solutions ofthe model is discussed analytically. The contact with nuclearstructure calculations, where the model can be used to grasp basicfeatures of the solutions of purely numerical treatments, isestablished by introducing realistic couplings constants.