In this paper, the formation of the excitonic insulator state in the rare-earth chalcogenides has been investigated through the extended Falicov-Kimball model. Adapting the unrestricted Hartree-Fock approximation, we have derived a set of explicitly self-consistent equations determining expectation values and the excitonic susceptibility in the system. Analyzing the excitonic susceptibility, we have established phase diagrams of the excitonic insulator state depending on the model parameters. The phase structures confirmed the excitonic insulator state is found at low temperature and between two critical values of the Coulomb interaction. The effect of the external pressure on the formation of the excitonic insulator state is also shown.
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