A generic model of the hybrid system mainly consisting of a solid oxide fuel cell (SOFC) and a heat engine is established, in which some main irreversibilities existing in real hybrid systems are considered. On the basis of the developed models of the SOFC and Brayton cycle with a regenerative process, analytical expressions for the power outputs and efficiencies of the subsystems and hybrid system are derived. It is found that for given parameters, the maximum power density of the hybrid system may attain 3.24 times of that of a single SOFC. Moreover, the general performance characteristics of the hybrid system are revealed and the optimal criteria of some of the main operating parameters are determined. The influence of the regenerative process in the heat engine is discussed in detail. It shows that through the introduction of a regenerator in the heat engine, the maximum power output of the hybrid system under the ideal regenerative condition will increase 51.51%. It is important to note that the results obtained here may be directly used to reveal the general performance characteristics of some special interesting hybrid systems consisting of a SOFC and a gas turbine or a Carnot heat engine.