Owing to climate change, natural events with low probability but high impact, such as storms, flooding, extreme precipitation, heat waves, have an increasing frequency. Meanwhile, the integration of various energy vectors, particularly electricity and natural gas systems, has widely grown in recent years. Many technologies, for instance, combined heat and power, energy hubs, and electrolysis, enable the increasing coupling of multiple energy infrastructure, improving system flexibility and reliability. However, for interconnected systems, any failures in one system could propagate to other energy systems, causing significant cascading energy loss. Thus, the security of integrated electricity and natural gas systems under extreme weather should be better managed from an integrated perspective, where the concept of resilience emerges. From the perspective of mitigating system loss and reducing system recovering time, this thesis designs a resilient energy system that absorbs negative impact in the disruption stage and allows efficient recovery operations during the post-disruption stage. To evaluate system behaviours under extreme stress, Chapter 2 presents a comprehensive scheme of vulnerability assessment for multi-energy systems, including both electricity and natural gas systems. Different from conventional vulnerability assessment methods, this scheme employs a modified PageRank algorithm, which not only refers to the structural importance of complex systems but also considers the impact of energy flow conditions within the entire network. After accomplishing vulnerability assessment methods, the impact of a specific catastrophe on an integrated energy system is simulated and quantified in Chapter 3. Subsequently, this section proposes a methodology to evaluate the impact of seismic events on the security of integrated electricity and gas system, mainly focusing on pipelines leakage and connection loss of electricity substation/lines. A stochastic model and probability model are used to formulate the damage level based on earthquake severity. The seismic impact on the integrated system is classified by relating to pipe leak and electricity line failure. Load curtailment due to limited generation capacity and overloading transmission lines can be obtained. The seismic intensity is generated randomly based on Monte Carlo simulation so that a certain seismic intensity can be related to relevant load curtailment. Thus, this research can inform the design of more cost-efficient resilience enhancement schemes for mitigating seismic events, thus enhancing the supply security of integrated energy systems. In the post-disruption recovery stage, to effectively mitigate system load loss and recovery time under hurricane stress, Chapter 4 and 5 then propose a new combined reconfiguration and operation method to enhance resilience for integrated energy systems. Systems are sectionalized and reconfigured by using natural gas valves, switches, and soft open points, energy storage, combined heat pump and electrolyser are operated to maximize the supply during the stress. To evaluate the efficiency of the proposed method, a resilience index that reflects both load loss and system recovery time is proposed. The proposed approaches can benefit both the system operators and customers with enhanced network security, reduced operation cost but low bills. The network and generation can both be strenghthened to protect the society's lifeline. On the basis of this scheme, the energy supply of the whole system under extreme conditions would be promoted, so that the negative impact to customers and network owners can be mitigated.