Provided are a computer program product, system, and method for sharing alias addresses among logical devices by a host accessing logical devices provisioned with a capacity from physical devices managed by a control unit. The host establishes with the control unit an association of logical devices and alias addresses assigned to the logical devices, wherein the alias addresses are associated with an alias management group. Alias address pool information is generated indicating each of the logical devices and their assigned alias addresses indicated in the association. The host uses from the alias address pool information any one of the alias addresses in the alias address pool information to access any of the logical devices associated with the same alias management group as the alias address.