In order to decarbonize the energy sector, the share of installed power plants based on renewable energy sources is increasing, as well as new gas thermal power plants in order to support the balancing of the power system. In addition, a relatively new, so-called power-to-gas (P2G) technology is recognized as one of the key factors that will enable the decarbonization of the energy system and help the power system integrate power plants with renewable energy sources. In any case, it is to be expected that the interdependencies of the electric power and gas systems will grow significantly in the coming period. Therefore, it is necessary to have robust simulation models that will efficiently and simultaneously calculate all connected energy networks in only one simulation environment and only one step. As a response to the described computational challenges, as part of the doctoral dissertation, a stationary model of a multi-energy system consisting of connected electric power and gas networks was developed, using the method of electrical analogy. Accordingly, detailed replacement electrical models of gas compressor and metering-reduction stations, as two of the three most important components of gas networks, were developed. The third component is the gas pipelines whose stationary electric substitute model is known in the literature. In addition, in order to simulate the power flows of a multi-energy system, additional electrical substitute models were developed, using the method of network poles, for all three components of the gas networks, as well as for the gas thermal power plant and the P2G plant. The electrical replacement models developed in this way were loaded into the well-known program package for the analysis of power networks - NEPLAN, and in this way the electrical 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 provided by the well-known commercial program package for the analysis of gas networks - SIMONE, and by comparing them with measurements from a real gas network. In addition, the practicality and advantage of using the applied multi-energy system modeling methodology on the example of security of supply analysis of integrated energy systems is presented.