Supply chain disruption risk usually poses a serious challenge to the management of emergency supplies procurement between the government and enterprises in cooperation. To research the impact of supply chain disruption on the supply and demand sides of emergency supplies for disaster relief, the emergency procurement model based on quantity flexibility contract is constructed. The model introduces a stockout disruption to measure the degree of supply chain disruption and uses per unit of material relief value to quantify government disaster relief benefits. Further, it analyzes the basic pricing strategy and the agreed order quantity between the government and enterprises, focusing on the negative impact of supply disruption on the government and enterprises. The model deduction and data analysis results show that supply disruption creates a “lose-lose” situation for governments and enterprises, reducing their benefits and willingness to cooperate. Finally, a sensitivity analysis is conducted on the case data to explain the decision-making changes in the contract price and flexibility parameters between the government and enterprises before and after the supply disruption.