The interest for the vocal fold modeling and in numerical simulations of voice production has arised due to the need to better understand the basic physics of voiced speech and to provide diagnosis and treatment for people with voice disorders. Different models have been proposed and used for both clinical and scientific research studies. Lumped-element models of the vocal fold viscoelastic structure coupled with various aerodynamic and acoustical models have proved to be one of the most useful approaches. On the other hand, the port-Hamiltonian systems (PHS) approach provides a powerful tool for analysis, modeling and control of complex dynamical systems. The approach is based on an energy point of view of systems and has been used in several applications. In this paper, we apply the port-Hamiltonian systems approach to model the voice production system. In particular, we obtain a switching PHS, for a body-cover model of the vocal folds. The resulting model explicitly shows the energy storage, energy dissipation and the interconnection underlying in the system. Additionally, different discretization of the obtained model are discussed.