Establishing cooperation agreements with enterprises on material reserves and emergency supply has become an inevitable choice for the government authority to enhance its emergency material supply capacity. Notably, when the government emergency management department uses contract mechanisms to improve the socialized reserve capacity, it is necessary to consider the huge demand for the emergency materials, the limited capacity of the local enterprises, and the possibility of the local enterprise’s reserve damage. This is because, from the perspectives of timely and economically supplying emergency materials, the local government authorities commonly prioritize establishing agreement cooperation with the local enterprises even if they may be directly affected by disasters. Correspondingly, whether it is necessary to introduce non-local enterprises to establish trans-regional emergency material supply agreement cooperation, and how to guide non-local enterprises to participate in the agreement cooperation have become urgent issues that the government authority needs to solve. Aiming to address the above-mentioned issues, this paper constructs a government-enterprise agreement cooperation model under the framework of quantity flexibility contract, where the local enterprise acts as the main supplier and the non-local enterprise acts as the backup supplier based on the principle of "near first and then far" for emergency material supply. Reverse derivation method is used to solve the government-led Stackelberg game model, where the enterprises’ optimal decisions on the flexibility supply quantity and the government’s optimal decisions on the flexibility procurement prices are analyzed successively. To validate and illustrate the necessity and benefits of trans-regional government-enterprise agreement cooperation, this paper further compares the government authority’s and enterprises’ decisions and costs/profits in the context of trans-regional agreement cooperation and the context of non-establishment of trans-regional agreement cooperation. Numerical experiments are then adopted to propose more properties, with sensitivity analyses being used to discuss the impacts of the disaster occurrence probability and the capacities of the local enterprise and the non-local enterprise on the optimal decisions and costs/profits of the government authority and the enterprises. Based on the findings generated from analytical derivation and numerical analysis, this paper puts forward the following two main managerial insights, which can be adopted by the government authority to economically establish and increase the reserve capacity in reality. (1) Introducing the non-local enterprises to participate in the emergency material reserve and supply not only can effectively alleviate the problems of delayed response to sudden demands and high costs caused by insufficient local reserve and supply capacity, but also can reduce the "monopoly" ability of the local enterprises by joining "competitors". Specifically, when the cost difference between the local enterprises and the non-local enterprises is not significant, the government emergency management departments in disaster-prone areas can induce the non-local enterprises to join in the reserve cooperation with a price that is lower than the price to induce the local enterprises. (2) Increasing the enterprise’s storage capacity helps the government improve its emergency material supply capacity and reduce the number of cooperative enterprises. However, for the government emergency management departments in areas prone to major disasters, even if the local enterprises have high storage capacity, it is not suitable to guide them to reserve a large amount of emergency supplies. Overall, establishing a small amount of reserve agreement cooperation with the local enterprises while establishing trans-regional emergency material supply agreement cooperation with the non-local enterprises is the best choice for the government emergency management departments. This is because, this kind of reserve cooperation strategy can help reduce economic losses caused by the damaged reserves due to disasters, avoid insufficient response capacity to sudden demands, and ultimately achieve the goal of the government emergency management department being able to meet the emergency material demand in a timely and cost-effective manner.