After an earthquake, the urgency of material needs at affected sites varies across different post-earthquake emergency stages. To maximize the temporal utility value of emergency supplies and ensure their effective use in rescue operations despite limited post-earthquake transportation capacity, this paper proposes a multi-stage post-earthquake emergency material urgency evaluation method. This study examines the changes in materials during the emergency response, divides the emergency response stages, and comprehensively considers indicators such as material durability, life hazard degree, irreplaceability, demand volume, and demand gap rate to construct a more suitable urgency evaluation system reflecting post-earthquake characteristics. Additionally, the improved TOPSIS-CRITIC evaluation method is introduced to scientifically quantify the urgency of material needs at affected sites during different emergency stages. An empirical study of the Wenchuan earthquake demonstrates that this method can effectively quantify the urgency of different types of materials at various stages and achieve priority ranking for material dispatch across different stages, thereby improving the efficiency of emergency rescue operations.