To ensure the supply of materials after urgent events, including recent public health crisis, it is crucial to formulate a reasonable preventive strategy for the location and distribution of emergency materials within the logistics network. In this paper, a class of multi-category emergency material storage distribution models under scenarios with uncertain post-event demand distribution is studied. Based on historical small-sample post-event demand information, the model constructs a two-stage material storage and scheduling distributionally robust optimization model. By applying a dual method, the non-linear distributionally robust optimization is transformed into linear optimization, and an improved Lagrangian L-shaped algorithm is designed to solve the two-stage model. Finally, the robustness of the model and algorithm is verified by implementing the method to a numerical example, and the sensitivity of the location and  distribution decisions to material shortage under different levels of urgent events is analyzed.