A mass exchanger 10 for storing blood, a blood product, packed cells. Exchanger 10 comprises an external casing 11 having at least one flexible wall. A cavity is provided in the casing 11 and has a region for blood storage and one or more channels 20 for accommodating flow of a treatment fluid. The one or more channels 20 are at least partly bounded by a permeable membrane 15, allowing the transfer of chemical species between the channel 20 and the cavity. The blood storing region may comprise a bag with at least one flexible wall. The permeable-membrane 15 may be permeable to gas, but impermeable to liquids, ionic or dissolved species. The exchanger 10 may comprise an indicator whose optical properties vary with blood composition. The exchanger 10 may serve as a heat exchanger, using the treatment-fluid temperature to maintain blood temperature. A method of storing blood comprising: introducing blood into exchanger 10 storing blood for a storage period and introducing treatment-fluid to modify blood composition. After the storage-period, the exchanger 10 may be transferred to a drip line head for blood transfusion. The method may select treatment-fluid composition to control blood concentrations of oxygen and/or carbon dioxide.