This paper reports on the development of a control-oriented model for simulating a hybrid auxiliary power unit (APU) equipped with a solid oxide fuel cell (SOFC) stack. Such a work is motivated by the strong interest devoted to SOFC technology due to its highly appealing potentialities in terms of fuel savings, fuel flexibility, cogeneration, low-pollution and low-noise operation. In this context, the availability of a model with acceptable computational burden and satisfactory accuracy can significantly enhance both system and control strategy design phases for APUs destined to a wide application area (e.g., mild-hybrid cars, trains, ships, and airplanes). The core part of the model is the SOFC stack, surrounded by a number of ancillary devices: air compressor/blower, regulating pressure valves, heat exchangers, prereformer, and postburner. Since the thermal dynamics is clearly the slowest one, a lumped-capacity model is proposed to describe the response of SOFC and heat exchangers to load (i.e., operating current) variation. The stack model takes into account the dependence of stack voltage on operating temperature, thus adequately describing the typical voltage undershoot following a decrease in load demand. On the other hand, due to their faster dynamics the mass transfer and electrochemistry processes are assumed instantaneous. The hybridizing device, whose main purpose is to assist the SOFC system (i.e., stack and ancillaries) during transient conditions, consists of a lead-acid battery pack. Battery power dependence on current is modeled, taking into account the influence of actual state of charge on open circuit voltage and internal resistance. The developed APU model was tested by simulating typical auxiliary power demand profiles for a heavy-duty truck in parked-idling phases. Suited control strategies also were developed to avoid operating the SOFC stack under severe thermal transients and, at the same time, to guarantee a charge sustaining operation of the battery pack. In order to assess the benefits achievable by introducing the SOFC-APU on board of a commercial truck, the simulated fuel consumption was compared with the fuel consumed by idling the thermal engine. From the simulation carried out, it emerges how the SOFC-APU allows achieving a potential reduction in fuel consumption of up to 70%.