This study presents a framework designed to enhance the location and allocation of relief supplies to earthquake-affected areas. Initially, the framework incorporates various types of relief supplies, delivery modes, multiple periods, and addresses the uncertainties of supply-demand scenarios following an earthquake. This leads to the development of a stochastic programming model that aims to minimize total costs while determining the optimal locations and distribution strategies. Further, the model undergoes a transformation to consider uncertainties under the framework of chance constraints, and the Gurobi solver is applied to solve the model. An illustrative example using the context of Mianyang City post-Wenchuan earthquake validates the model's adaptability. It demonstrates effectiveness amidst dynamic changes in multi-period road network damage and fluctuating supply-demand scenarios. The study also compares the performance of the stochastic planning model with a deterministic planning model through comprehensive numerical results. The evaluation reveals that in practical scenarios, where quantifying the total emergency supplies or demand from individual disaster-affected areas is challenging, our stochastic model outperforms deterministic models. It provides effective solutions for emergency facility locations and multi-material allocations.