Apparatus (1) for storing energy includes a high pressure storage vessel (10) for receiving high pressure gas, the high pressure storage vessel (10) including a high pressure heat store including a first chamber housing a first gas-permeable heat storage structure (14); and a low pressure storage vessel (11,12) for receiving low pressure gas, the low pressure storage vessel (11,12) including a low pressure heat store including a second chamber housing a second gas-permeable heat storage structure (16,18. The first heat storage structure (14) has a mean surface area per unit volume which is higher than a mean surface area per unit volume of the second heat storage structure (16,18).