In team chess, Šulskis has participated in the Chess Olympiad representing Lithuania multiple times from 1996 to 2016. He has also been part of the Lithuanian team in the World Team Chess Championship and several European Team Chess Championships.
Šulskis has performed well not only in classical chess, but also in rapid chess. In 2010, he won the Lithuanian Rapid Championships, and has been successful in other international rapid events too.
Notably, he was on the winning team of the European Club Cup in 2009, playing for the Saint-Petersburg Chess Federation. Despite his chess career, Šulskis is also a business and public administration graduate from Klaipėda University in Lithuania.