This paper proposes an optimal siting and sizing method for distributed energy storage in distribution networks considering islanding duration uncertainty. The uncertainty of the islanding duration is described based on robust optimization, which improves the ability of islanding operation and guarantees the un interrupted power supply of important loads. The planning model aims to minimize the sum of the annual investment cost of energy storage, the annual power purchase cost of the distribution network, and the operation and maintenance cost of energy storage, the configuration and operation constraints of distributed energy storage, photovoltaic output constraints, distribution network flow constraints, grid operation safety constraints, power purchase constraints and load power supply constraints and the uncertainty of islanding duration is considered in the planning model. The column?and?constraint generation algorithm (C&CG) is adopted to solve the mixed?integer second?order cone robust programming model. The planning model is carried out under an actual distribution network. The results show that the established model can optimize the planning solution of distributed energy storage while guarantee the power supply of important loads considering the islanding duration uncertainty, and improves the ability of distribution network islanding operation and economy