A brake arrangement is provided for a mobile storage unit having a drive arrangement for causing movement of the mobile storage unit. The brake arrangement has a brake member mounted to and rotatable with a drive shaft of the drive arrangement, and acts on the drive shaft when the input force on the drive shaft is relieved. A flexible band is engaged with the brake member and defines a pair of ends that are engaged with a tensioning mechanism. The tensioning mechanism applies a tensioning force to the ends of the brake band to tension the brake band against the brake member to inhibit rotation of the drive shaft and thus movement of the mobile storage unit when the input force is relieved.