Petroleum is the pillar industry of the national economy, but safety accidents are frequent all over the world. The government attaches more importance to the safety production management of enterprises to reduce the occurrence of accidents that infringe on personal safety. The management of emergency supplies, which can effectively respond to the occurrence of safety production accidents, is a key measure for handling emergency accidents. Rapid response to accidents means reducing accident rescue costs and protecting personal and property safety. This paper proposes a material stochastic model with the randomness of accident demand for materials. The enterprise and the government can obtain the material management scheme and the quantitative evaluation standard of accident preventive measures from the model results respectively. The model covers as many accident scenarios as possible through multi-scenario modeling to reduce the impact of accident uncertainty. Finally, the feasibility is proved by an example of a petroleum enterprise in Zhoushan City. When the accident demand fluctuates randomly between 80% and 120%, the model proposes a material management scheme that the dispatching time of materials and the cost in rescue work do not exceed 31.33 min and 11.68 million CNY respectively. With the assistance of the model, the enterprise saves the cost of safe production and improves the efficiency of rescue. The government has strengthened the supervision and evaluation of enterprise safety production management. Finally, the mission of protecting the property and life safety of the people will be realized.