The fuel cells are the technology of the future. Although their discovery dates back to the 19th century the nature of how they work hasnt been adequately explained so far. This thesis focuses on description of solid oxides fuel cells (SOFC) for which ion conductive electrolyte and high operating temperature are distinctive. The mathematical model of SOFC developed in this thesis is formulated in terms of the mixture theory. The model development was constrained and simplified by isothermality, time-stationery and 1D approximation. The model equations characterize gas and ion transport and electric current flow in the fuel cell. Eventually comparison of the thesis model equations with the SOEC (solid oxides electrolysis cell) model developed at the Institute of Chemical Technology in Prague showed that both approaches lead to a similar conclusion. This thesis can be used as a basis for an experimental verification of the mixture theory.
