As a critical resource in emergency response and a pivotal element in disaster prevention and risk reduction, shelters play a central role in the holistic continuum of rescue and relief efforts. However, existing research often overlooks the comprehensive assessment and enhancement of shelter resilience. This study proposes a novel safety–robustness–accessibility (SRA) model aimed at evaluating and enhancing the overall resilience of shelters in the face of disasters. Firstly, a resilience assessment system for shelters was established, leveraging multi-source data and encompassing diverse dimensions, including safety, robustness, and accessibility. Subsequently, the entropy weight method was utilized to determine the weights of the assessment indicators. The case study and comparative analysis were conducted on shelters situated in two urban areas, old and new, in Kunming City, China, namely Wuhua District and Chenggong District. The findings reveal a higher quantity of shelters in Wuhua District compared to Chenggong District; however, the overall resilience level is relatively low, predominantly categorized as “Mid-Low” grade, constituting a substantial 57.94%. Conversely, shelters in Chenggong District exhibit a relatively high resilience level, predominantly classified as “Medium” grade, accounting for 33.77%. This study furnishes valuable data references and specific strategies aimed at enhancing the resilience of urban shelters against disasters. It offers crucial insights for urban planning and management to strengthen shelter resilience, thereby contributing to the development of a more resilient and sustainable urban future.