Multi-carrier energy systems (MCESs) provide collaboration between various kinds of energy carriers to supply the electricity, heating, and cooling demands. With the widespread use of MCESs in recent years, the security assessment of energy systems has attracted the attention of many contemporary researchers. However, the complexity of an MCES, including electrical, natural gas, and district heating networks, and different uncertainties imposes vast challenges to keep a safe operation energy supply. In this paper, a systematic methodology for the security analysis of MCESs is presented. For this purpose, considering electrical, natural gas, and district heating networks, an integrated model of energy systems is introduced. The security analysis of this framework is evaluated using some indices. In this approach, two well-known performance indices, including power performance index (PIP) and voltage performance index (PIV), are used to analyze the electrical networks’ security. Besides, the concept of Energy not supplied (ENS) is used for natural gas and district heating networks. In this regard, security analysis of a typical MCES including the IEEE 14-bus electrical network, the IEEE 30-bus electrical network, 20-node Belgian natural gas network, and 14-node district heating network is examined. The applicability of the proposed technique will be proven using comprehensive simulation analysis.