In order to decarbonize the energy sector, the installation of the intermittent renewable energy sources (RES) in the power system is growing, as well as the new gas-fired power plants (GFPPs) for the balancing purposes. Furthermore, power-to-gas (P2G) technology is recognized as one of the key contributors to provide decarbonization of the energy sector, and as a help to the power system with integration of the increasing share of RES. In any case, the interdependencies between the power and natural gas systems are going to be much stronger in the next period. Thus, it is necessary to have a powerful simulation model that is able to efficiently and simultaneously solve all coupled energy carriers in a single simulation environment in only one simulation step. As an answer to the described computational challenges, a unique model for the steady-state analysis of a multi-energy system (MES), consisted of coupled the power and natural gas networks, using the electrical analogy approach is developed. Accordingly, detailed electrical equivalent models of gas compressor and pressure reducing and metering stations have been developed, as two of the three most important components of gas networks. The third component is the gas pipeline, whose steady-state electrical equivalent model is known in the literature. Besides, in order to perform load flow simulation of the multi-energy system, additional electrical equivalent models have been developed, using the network port theory, of the most important natural gas network elements, as well as of the GFPP and P2G. The presented models were loaded up into well-known software for the power system simulation – NEPLAN, and in that way, an electric model of a multi-energy system was formed. The accuracy of the developed models of gas network elements was confirmed by comparing the simulation results with the results obtained by the well-known commercial software package for gas network analysis – SIMONE, as well as with the real natural gas network measurements. In addition, the practicality and advantage of using the applied methodology of multi-energy system modeling on the example of security of supply analysis of integrated energy systems are shown.