Abstract: A heat or cold storage multilayer tower has athermo-insulated housing with a multilayer system of rigid blocks, Each rigid block has a set of narrow vertical ducts, when these narrow ducts are alternatively open or provided with sealed flexible bags, which are ufabricated from polymer film or metal foil and contain a phase change material (PCM). The rigid block are fabricated from ceramics, glass, glass ceramics, polymer fibro reinforced concrete or glass-fiber reinforced concrete. Hydrostatic pressure of molten PCM in the sealed flexible bags ensures good thermal contact of the sealed flexible bags with internal walls of the corresponding ducts. This construction provides effective heat transfer between a heat transfer fluid (HTF) and PCM in the processes of charging and discharging of the sealed flexible bags with heat or coldwith high values of stored thermal energy for specific volume.