This paper primarily focuses on the formulation and validation of mathematical and numerical models for a new electrolyte-supported solid oxide fuel cell stack. By leveraging numerical modeling, the main goal is to deepen the understanding of the operational aspects and transport phenomena within this system. The developed models are implemented in ANSYS, Inc., Fluent software, which enables a range of simulations. To validate the models, a stack fabrication methodology, a prototype construction, and conducted electrochemical tests were proposed. The simulated current-voltage characteristics for two different operating temperatures and three different fuel compositions were compared with the experimental measurements with satisfactory agreement. The counter-flow configuration was simulated and compared to the co-flow arrangement. The numerical simulation has demonstrated its efficacy in identifying possible design imperfections and enhancing the operational conditions of the prototype stack. Moreover, the developed model was further used, in Part 2 of this paper, to analyze the improvement options implementation for the next stage of the prototype.