Quite a lot of Sony Xperia phones released in 2012 lack the Mass Storage Mode or the USB Mode. These phones comes with MTP mode which definitely has its advantages over USB mass storage. But the lack of this mode is a big issue for users. Not only is USB mass storage faster, it would be good if there is an option to switch between the modes.
Here is an app called SD Mounter by XDA Senior Member Soheil_rf that enables mass storage developed on the Xperia S, P and U running Ice Cream Sandwich and Jelly Bean.
SD Mounter allows users to easily activate either mass storage mode or media transfer mode. But the downside is that you will need s rooted device with busybox is required for it to operate properly.
More details and the download link available in the XDA thread here.