[Sony Xperia Tablet Z] Rooting Model SGP311

 The chinese app at this russian site worked for me.

http://sony-xperia.mobi/programmy/247-poluchenie-root-dlya-xperia-tablet-z-dlya-proshivok-10-3-1-c-0-136-sgp311-312-i-10-3-1-a-0-244-sgp321.html

You need to install the app on your pc, and connect Xperia Tablet Z to your pc using USB.

However, please ensure usb debugging mode is enabled by
1) Tapping on "Settings > About Tablet > Build Number" multiple times to reveal the "Developer Options" in Settings.
2) Ensure " Settings > Developer options > USB debugging " is CHECKED.

Reference:
http://forum.xda-developers.com/showthread.php?t=2428830&page=2