With the deepening of the coupling between the electric power system (EPS) and the natural gas system (NGS), an issue that the gas pressure instability precedes the voltage instability may appear in the integrated electricity-gas system (IEGS). Load shedding is the final guarantee to ensure the stability of the system. Unlike single type of load in EPS, there are two kinds of load in IEGS: electricity and gas. To reduce the overall load loss of IEGS, it is necessary to quantitatively evaluate the impact of load shedding across electricity and gas systems. A minimum load shedding method in the IEGS based on the sensitivity method is proposed in this paper. Firstly, based on the continuous multi-energy flow model, the critical operating point of IEGS gas pressure stability is located, and the node where the gas pressure first becomes unstable is regarded as the weak link. Secondly, the sensitivity index of the weak gas pressure to the electric and gas load is constructed based on the Jacobian matrix at the critical operating point to evaluate the recovery effect of shedding load at each node on the weak gas pressure. Then, the load is shed in descending order of the sensitivity index to restore the IEGS with a sufficient gas pressure margin through the least load loss. Finally, the necessity of considering cross-system load shedding and the effectiveness of this method in reducing the amount of load shedding are verified by case studies.