As a high proportion of renewable energy is connected, the reliable and stable operation of distribution network is affected by multiple uncertain factors. Therefore, an energy storage siting and sizing optimization method is proposed that considers the reliability and vulnerability of distribution network. Firstly, taking into account the uncertainty of wind and photovoltaic power and load, the improved K-means clustering algorithm and synchronous backtracking elimination algorithm are used to obtain the uncertain operation scene set. Then, the idle capacity and power of energy storage are optimized to participate in the energy market and frequency modulation auxiliary service market, and the operation plan of energy storage system is revised. Secondly, an energy storage multi-objective programming model is established, which takes the annual comprehensive cost of distribution network, the expected value of the system power shortage and the comprehensive vulnerability index of distribution network as the optimization objectives. At the same time, considering the availability of energy storage system on the basis of load transfer, the reliability evaluation method of distribution network based on optimization model is used to calculate the reliability index. Finally, the multi-objective differential evolution algorithm based on Tent chaotic mapping and adaptive mutation strategy is used to solve the model. The advantages of the proposed model and algorithm are verified by setting different schemes through the numerical simulation analysis of IEEE 33-node distribution system.