Public acceptance is important for the provision of potentially hazardous facilities and may be affected by many factors such as perceived risk/benefit/stress/fairness and public trust. In this study, the underlying mechanism behind the influence of perceived stress on public acceptance of waste-to-energy (WTE) incinerators was explored by structural equation modeling of a face-to-face questionnaire survey of 1066 urban residents in three regional central cities in China. The results indicate that, firstly, the perceived stress of the laypeople has an impact on their acceptance by influencing risk/fairness they perceived and public trust. Secondly, the paths of influence of individual perceptions on acceptance differ between cities with different economic, cultural, and social characteristics. Perceived stress mainly affects public acceptance through perceived risk in the eastern residents while perceived stress mainly affects public acceptance through public trust in the western residents. The findings clarify the theoretical role of perceived stress in shaping laypeople’s acceptance of potentially hazardous facilities which are of value for both governments and owners in siting potentially hazardous facilities.