Abstract: In order to meet the low-carbon operation requirements of the integrated electricity and natural gas systems (IEGSs) with various uncertain factors under the dual-carbon target, a low-carbon probabilistic optimal energy flow model for IEGSs is developed in this paper, and a decoupling cross-terms based stochastic response surface method (SRSM) is proposed to solve this model efficiently. First, the lower-carbon cooperative operation mechanism between carbon capture and power-to-gas devices is constructed, which can realize carbon recycling and multi-mode cooperative utilization of hydrogen. Then, the low-carbon probabilistic optimal energy flow model for IEGSs is established. Since the existing probability analysis methods of IEGSs are difficult to balance calculation accuracy and efficiency, a probabilistic optimal energy flow analysis method based on SRSM improved by decoupling cross-terms is proposed. The Taylor series expansion is used to decouple and simplify the cross-terms in Wiener polynomial chaos. The difficulty of dealing with high-dimensional random variables by SRSM is overcome. Finally, the accuracy and adaptability of the proposed model and method are verified by using the IEEE 39-NGS 20 and IEEE 118-NGS 90 standard test systems.