A finite-volume based mathematical model has been developed for modeling hydrogen production by a tubular cell of solid oxide steam electrolyzer (SOSE), taking into account the electrochemical reactions and heat/mass transfer effects. The model is composed of three systems of nonlinear equations that govern the electric current density, energy balance in the solid SOSE cell, and energy balance in the flow of steam and hydrogen. The simulated hydrogen production rate proportional to the applied potential agreed well with the experimental measurements published in the literature. The intermediate modeling results indicated that the activation effect dominate the overall cell overpotential due to low exchange current density through the SOSE cell electrodes. Thus, higher electrode activity was identified as an important factor for enhancing cell performance. Parametric modeling analyses were conducted to gain better understanding of the SOSE characteristics. It was found that low-temperature gas intake would cause a high temperature gradient in the tubular cell material at the inlet, possibly leading to a thermal expansion problem. The risk could be reduced by increasing the gas inlet temperature. It was also found that energy-efficient SOSE hydrogen production can be achieved by reducing the hydrogen content in the steam intake and regulating the steam intake flow rate to an optimum that minimizes the overall electrical and thermal requirements. More parametric modeling results are discussed in this paper. The tubular SOSE cell model developed in this study can easily be expanded to accomplish tubular SOSE stack analysis for comprehensive system design optimization.