The aim of this study is to perform a numerical analysis of the influence of the position of the tubes carrying the heat transfer fluid on the charging and discharging processes of a thermal energy storage system with a phase change material (PCM). The investigation was based on a three-dimensional numerical model of a repetitive section of the storage unit, consisting of four copper tubes and an aluminium fin acting as a heat exchanger. The model was implemented in the ANSYS Fluent environment using the built-in Solidification and Melting Model, which accounts for heat conduction, natural convection in the liquid phase, and the phase change of the PCM. Several configurations of tube placement were analysed with respect to the vertical position within the storage unit. The study evaluated their impact on the charging and discharging time, the resulting heat fluxes, temperature distribution, and the evolution of the liquid phase fraction over time. In the simulations, a PCM with a relatively high phase change temperature of approximately 78°C was used, allowing the results to be applicable in the design of thermal storage systems integrated with conventional central heating installations. The results indicate that tube placement significantly affects the efficiency of the charging process. Lowering the tubes toward the bottom of the storage tank reduced the melting time of the PCM by 23.2%, mainly due to the enhancement of natural convection. In contrast, during the discharging process, the tube arrangement had a significantly smaller impact on the solidification time. The findings of this analysis may serve as a basis for designing more efficient stationary and mobile PCM-based thermal energy storage systems, especially in applications where compactness and fast thermal response are essential.