The energy sector is focused on gradual transition toward climate neutral solutions. To this end, the improvement of power generation technologies and replacing conventional methods with greener options are areas of keen interest. One group of solutions currently under development are cogeneration systems based on solid oxide fuel cells (SOFC), which are now available commercially. Although power installations with SOFC exhibit higher electrical efficiency compared to conventional power plants (in excess of 50-65% versus the efficiency of thermal cycles in the range of 38 to 63%), there is still space for improvement. One of the technical measures to boost efficiency in SOFC-based systems is to recycle anodic off-gas. In this paper, recirculation of anodic gas in a 10 kW SOFC system was studied using a numerical model. Several configurations of the system with SOFCs were under consideration. The model of a system with blower-driven anodic off-gas recirculation was developed and implemented in Aspen HYSYS modeling software. Two alternative fuels natural gas (NG) and hydrogen were considered for the stack with anode supported SOFCs. Main system parameters including net power and electrical efficiency are presented for multiple operation points with different recirculation ratio and fuel utilization factors. Operating conditions were defined based on experimental investigation of SOFC stacks carried out at the Institute of Power Engineering. A comparison with a reference system without recirculation is shown.