The regular lockdown policy adopted in controlling the pandemic of COVID-19 has caused logistic disruptions in some areas that have a great impact on the living standards of residents and the production of enterprises. Given that the construction of emergency logistics centers is an effective solution, this paper takes the Yangtze River Delta Area (YRDA) of China as an example and discusses the site selection and material distribution of the emergency logistics centers in the region via a two-stage model. The first stage is the selection of candidate emergency logistics centers in the YRDA. A comprehensive evaluation index system is built with 4 primary and 15 secondary indexes to evaluate the logistic infrastructure capacity of the 41 cities in the YRDA. Further, through a principal component analysis, 12 cities are selected as candidate construction sites for emergency logistics centers. In the second stage, a biobjective site selection model with uncertain demand is established and calculated via the NSGA-II algorithm. According to the time sensitivity of emergency logistics, six cities are filtered from the optimal solution set, including Hefei, Hangzhou, Xuzhou, Wenzhou, Changzhou, and Shanghai, ensuring that all 41 cities are within their service scope.