Driven by the growing threat of natural disasters caused by climate change, there is an urgent need to strengthen the emergency rescue logistics network. However, insufficient research has been conducted on optimizing both pre-disaster preparation and post-disaster response, resulting in lower resilience and inefficiency of emergency logistics management. To this end, this study explores the optimization of emergency rescue resource allocation and transportation network design, considering the uncertainty and multi-period nature of natural disaster rescue. By employing a lateral transshipment strategy, a three-stage stochastic programming model is established, which aims to balance economic benefits with the need for devastations, thereby enhancing the resilience of the logistics network. Numerical experiments verify the effectiveness of the proposed model with different instances and the performance of the lateral transshipment strategy by comparing it with a two-stage stochastic programming model. Sensitivity analysis is performed on the costs of constructing a depot and the penalties for unmet needs. The analysis yielded valuable insights that can be used to enhance emergency rescue operations, supply chain network design, and logistics network design. The research outcome can benefit emergency responders and logistics professionals in optimizing their operations.