The deep interdependence between electrical and natural gas system has great influence on the security of multi-carrier energy (MCE) systems. The large-scale access to distribution generation (DG) of clean energy makes it necessary to investigate the effects of uncertainties on the safe and stable operation of MCE systems. However, the existing probabilistic energy flow analysis for MCE systems pays little attention to the difference between the correlation of various DG during calculating the energy flow. Therefore, this paper investigates the probabilistic energy flow considering the uncertainties and correlations of various DG. A framework of MCE systems considering various coupling units including power to gas (P2G) and energy hub is initially proposed. For this, the Monte Carlo simulation (MCS) method based on Latin hypercube sampling (LHS) and Nataf transformation is specially designed to calculate the energy flow for each sample. The energy flow calculation method is composed of three-phase AC/DC alternating iteration method and improved Newton node mesh method considering the control mode of compressors. Finally, the test system containing improved IEEE123-node system and NGS48-node system have verified the accuracy of the proposed probabilistic energy flow calculation method. INDEX TERMS Renewable-based multi-carrier energy systems, energy hub, probabilistic energy flow, Nataf transformation, Monte Carlo simulation.