Emergency shelters are a critical component of public safety and emergency management, fulfilling essential roles in the early warning and response to significant emergencies, rescue operations, and transitional resettlement processes. They are vital for risk transfer and avoidance, refugee settlement, and the maintenance of social stability. This study integrates the Gauss two-step mobile search method with the origin-destination (OD) cost matrix, focusing on the actual road network and utilizing evacuation time as a research threshold. The objective of this approach is to minimize discrepancies in the rational layout outcomes that arise from neglecting the interaction between supply and demand, as well as the actual distances considered in prior studies. The research examines the rationality of the layout of refuge locations from a supply and demand perspective. The findings suggest the following: (1) The accessibility of emergency shelters within the primary urban area of Chengdu generally satisfies the demand for refuge, with the three most accessible districts being Jinjiang, Qingyang, and Wuhou. (2) Despite a relatively even distribution of shelters, the central urban area of Chengdu experiences a deficiency in emergency shelters, particularly in densely populated regions located at the center of the research area, where spatial capacity is constrained. (3) As the duration of evacuation increases, the number of accessible emergency refuge locations for residents also rises; however, the substantial resident population in the central area, coupled with the static capacity of refuge facilities, results in a continual shortfall. These findings provide essential data and recommendations for the sustainable and effective development of emergency shelters in Chengdu, as well as for the enhancement of its disaster prevention and mitigation strategies.