The theoretical model of the solidification process of a shell-and-tube ice storage (STIS) device with longitudinal fins is established. The liquid fraction, the energy-discharging rate and the ice storage ratio are investigated, with particular focus on the effects of the fin structure parameters on the solidification process. Furthermore, the temperature and the streamline distributions are discussed to reveal the mechanism of the solidification process in the STIS device and the negative effect of natural convection (NC). It is indicated that the solidification process of the STIS device is dominated by the heat transfer via the fins at the beginning, and then by the heat transfer at the water-ice interface. The ice storage is negatively affected by the NC, for the reason that the water with a higher temperature stays in the lower part of the STIS device and the temperature gradient at the water-ice interface is small. The ice storage performance can be enhanced by increasing the fin structure parameters, including height, thickness and number.