The reliability evaluation of integrated power-gas systems (IPGS) becomes critical due to the high dependency of the two energy systems. Once a contingent incident happens in one system, the other system will accordingly be affected. In this paper, a detailed model for the IPGS is presented with the consideration of the power-to-gas devices and gas storages. Furthermore, a sequential Monte Carlo (SMC) simulation is utilized to evaluate the reliability of the IPGS. In particular, the gas storage life reliability model is considered to characterize the charging and discharging performance. Moreover, an optimal load shedding model is used to coordinate the load shedding of the IPGS. What's more, new reliability indices are given to display the reliability of the IPGS. Finally, the proposed model is tested on an integrated IEEE 24-bus power system and 20-node gas system and an integrated IEEE RTS 96 power system and 40-node gas system. The results show the effectiveness of the proposed model.