Based on Solid Oxide Fuel Cell (SOFC) technology, Solid Oxide Electrolysis Cell (SOEC) offers an interesting solution for mass hydrogen production. This study proposes a multiphysics model to predict the SOEC behavior, based on similar charge, mass, and heat transport phenomena as for SOFC. However, the mechanism of water steam reduction on Nickel/Yttria-Stabilized Zirconia (Ni/YSZ) cermet is not yet clearly identified. Therefore, a global approach is used for modeling. The simulated results demonstrated that a Butler–Volmer’s equation including concentration overpotential provides an acceptable estimation of the experimental electric performance under some operating conditions. These simulations highlighted three thermal operating modes of SOEC and showed that temperature distribution depends on gas feeding configurations.