System for handling dies with a rectangular and/or arched transverse cross-section that comprises a support for placing in a removable manner dies having a rectangular transverse cross-section, the support being designed to be coupled in a sliding manner to a fixed structure, in which at least said support has fastening means for holding at least one die with a rectangular transverse cross-section vertically in the air; and a handler provided with hooking means designed to be coupled to the support to place and/or remove the support with respect to the fixed structure, the handler having coupling means to be coupled to a transelevator or similar. This system is designed to facilitate the operations of placing and removing the dies during their storage.