Solid oxide electrolysis cells (SOECs) have great application prospects because of their excellent performance, but the long-term applications of the stacks are restricted by the structural degradation under the high-temperature conditions. Therefore, an SOEC degradation model is developed and embedded in a process model of the high-temperature steam electrolysis (HTSE) system to investigate the influence of the stack degradation at the system level. The sensitivity analysis and optimization were carried out to study the influence factors of the stack degradation and system hydrogen production efficiency and search for the optimal operating conditions to improve the hydrogen production efficiency and mitigate the stack degradation. The analysis results show that the high temperature and large current density can accelerate the stack degradation but improve the hydrogen production efficiency, while the high temperature gradually becomes unfavorable in the late stage. The low air-to-fuel feed ratio is beneficial to both the degradation rate and hydrogen production efficiency. The results show that the optimization method can improve the hydrogen production efficiency and inhibit the stack degradation effectively. Moreover, part of the hydrogen production efficiency has to be sacrificed in order to obtain a lower stack degradation rate.