Abstract: To address the problem of insufficient flexibility caused by the uncertainty of renewable energy and the fluctuation of multi-energy loads in regional integrated energy systems (RIES), this paper proposes a robust optimization method considering the flexibility of muti-energy complementarity and low-carbon willingness of users. Firstly, the flexibility demand of the power subsystem in RIES is characterized by net load fluctuations, which are influenced by both renewable energy output and load. To consider the impact of users' low-carbon willingness on renewable energy consumption, utility functions for purchasing normal and zero-carbon electricity are conducted, respectively. Considering the flexible reserve of multi-energy coupling devices, a three-layer robust optimal scheduling model with multi-energy flexible supply-demand balance constraints is established, aiming to minimize the total operating cost and maximize users' utility. The optimal operation range of devices is introduced to decouple time-coupling constraints, and Karush- Kuhn-Tucker (KKT) conditions and nested column and constraints generation (NC&CG) algorithm are to solve this model. The case study demonstrates that the proposed model can improve operating flexibility, promote the integration of renewable energy, and achieve low-carbon economic operation in RIES.