With the increasing attention of the clean and efficient use of energy, the regional integrated energy system (RIES), as an efficient measure to improve energy efficiency, is tending to play an important role in the field of energy supply. The configuration of multiple energy storage equipment in the RIES can greatly improve the economy of the system, which is an important research direction of RIES planning. However, at present the research on the configuration optimization of electric-gas-thermal multi-energy storage devices in RIES is insufficient. Under this background, a method for configuring the rated capacity and power of various energy storage devices in the RIES under both off-grid and grid-connected operating modes was proposed in this paper, and the configuration optimization model was also established. Firstly, the RIES was divided into four parts: Energy supply, energy conversion, energy storage and the load. Based on the energy hub concept, the four parts were modeled respectively. Secondly, considering the influence of electric energy substitution and operation strategy, the optimal configuration of multi-energy storage devices was modeled as a MILP formulation and solved with the Gurobi optimizer. Finally, a case study verified the effectiveness of the proposed model and the method. Furthermore, the sensitivity analysis was carried out to quantify the influence degree of each factor (such as price, etc.) on the energy storage configuration.