In this work, thermal energy storages based on granular phase change material with gaseous heat transfer fluid are studied to determine their optimal shape. The shape of the energy storage unit affects the gas dynamics in the object, and this affects the processes of heat transfer, heat accumulation and heat recovery. A novel numerical model is developed and used for investigating the gas-dynamic and thermophysical processes in packed bed thermal energy storages. Using numerical experiments, the effect of narrowing and expansion of side walls on charging and discharging processes of the energy storages is studied for two types of boundary conditions: the known input mass flow rate of the gas and the known gas pressure at the open boundaries of the object. To determine the most optimal shape of the thermal energy storage, several efficiency criteria are used. It is shown that preference of the storage shape at both charging and discharging processes depends on the choice of efficiency criterion and specific conditions of the process such as boundary conditions, phase change temperature of granular material, and so on. Narrowing or expanding thermal energy storages have advantages in rare cases; the storages with straight walls are often most preferable. (c) 2020 Elsevier Ltd. All rights reserved.