After arriving in France from Georgia in Fédérale 1 to play for Massy, Kubriashvili, aged 21, moved up the leagues to the Top 14 with Montpellier.

However, after one season there where he didn't get much game time, he moved to the newly promoted Toulon in 2008, where he has since established himself as a regular member of their squad and has played over 100 matches for the club.

In 2010, Toulon signed former All Black Carl Hayman who was seen as one of the best tighthead props in world rugby.

Kubriashvili made his debut for Georgia in 2008 against Portugal, but has largely had to play as second choice to Davit Zirakashvili through most of his international career.

In 2011 after a successful season for Toulon, Kubriashvili became the first Georgian to play for the Barbarians and he featured in their victories over England and Wales.