Recently, Heat-ESS, one of the key technologies to develop the energy storage and distribution system, is attracting attention because of its capability and usages in greenhouse gas reduction and energy efficiency improvement. In this study, transient numerical analysis was carried out on the thermal behavior of PCM in plain and internally finned tubes, which are the primary components of Heat-ESS system. The results show that the heat transfer via conduction is dominant initially and a thin layer of molten PCM was formed along the tube wall. As the layer expanded, circulating flow of the molten PCM occurred between the solid PCM and the tube wall, and natural convection plays important roles in the heat transfer. In order to evaluate the effects of the fin on the melting process, different length and number of fins were investigated. With increasing the length, the melting rate and heat flux increased, and showed maximum values of 0.0024 sec-1 and 7.14 kW/m2 at the length to radius ratio of 0.5, respectively. In addition, the melting rate increased with increasing the fin number. However, at the number of fins more than 8, heat flux began to decline, resulting in a decrease in heat transfer efficiency.