This paper sets out the results of mathematical modeling and numerical simulations with regard to the influences of the type and thickness of electrolyte on Solid Oxide Fuel Cell Hybrid System (SOFC-HS) performance. A change of electrolyte materials can result in total hybrid system efficiency increasing from around 48% HHV (53% LHV) to about 65% HHV (72% LHV) in an environment where turbine inlet temperature and gas turbine subsystem pressure ratio remain unchanged. The governing equations of SOFC-HS modeling are given. An adequate simulator of the SOFC stack was made and described. Based on this simulator, a model of the Siemens Westinghouse unit was built. The performance of this SOFC-HS with different electrolyte materials and thicknesses is shown, and some characteristics are given and described. The advantages and disadvantages of different electrolyte types from a hybrid system performance point of view are indicated.