The effects of subcooling and natural convection are studied numerically on the melting process of an initially subcooled phase-change medium filled inside a horizontal circular cylinder. It is postulated that melting continues with the tube wall kept at a constant temperature and with the unmelted solid core fixed. Primary emphasis is placed on the evolution of interface morphology, the local/overall heat transfer rate at the tube wall and at the interface, and the structure of natural convection. The numerical results are mainly presented in terms of the Rayleigh and subcooling numbers. As the degree of subcooling intensifies, the melting rate and the movement of the interface are impeded but the interfaces are of similar shape with the passage of time. The heat transfer characteristics are found to be mostly governed by the formation pattern of natural convection in the liquid phase. Good agreement with available experimental data is found.