It is possible to enable USB mass storage mode on Samsung Galaxy S4 using an app called SG USB Mass Storage Enabler which can be downloaded from the Google Play Store for free. This app exports you micro SD card as mass storage device and it works with all different variants of the Galaxy S4 such as LTE version (i9505) and international octa core variant (i9500). A user after the installation can also create a shortcut to quickly enable or disable the function. Please note that this do not work with the internal memory of the phone due to system limitations according to the author. Furthermore a root is required on your Samsung Galaxy S4 to make use of SG USB Mass Storage Enabler. BusyBox must also be installed on the device.

unnamed | Enable USB Mass Storage Mode on Samsung Galaxy S4

This app also works with the Samsung Galaxy SIII (GT-I9300, GT-I9305, SPH-L710),  Samsung Galaxy Note II (GT-N7100) and Samsung Grand Duos (GT-I9082). Here is the link to the app on the Google Play store.