Martynas Pocius was born in Vilnius to Gintaras, a basketball coach, and Jūratė, a physical education teacher.

Pocius was also named to the World Select team for the 2005 Nike Hoops Summit, where he scored a game high 20 points in a 98–106 loss to the USA.

Pocius led the team to the Baltic Basketball League (BBL) title, averaging 10.7 points, 2.9 rebounds and 0.9 assists.

He also led the team to a second place in Lietuvos krepšinio lyga (LKL), after losing the final's best-of-seven series 4–3.

Pocius finished the EuroLeague season averaging 10.8 points per game and helped Žalgiris Kaunas win the LKL championship, beating Lietuvos rytas Vilnius in the semifinals, and Neptūnas Klaipėda in the finals.

[4] After a difficult season where Pocius struggled with injuries and playing, and helping Žalgiris Kaunas to another LKL championship, he was loaned to UCAM Murcia.

On 16 June 2017, Pocius announced his retirement from professional basketball being just 31 years old due to injuries and pain he suffered while exercising.

He played in the 2004 European U-18 Championship in Spain, where he showed himself as a team leader, averaging 26 points, 3 rebounds and 2.3 assists.

Pocius also represented Lithuania at the 2006 European U-20 Championship in Turkey, where he led the team to a seventh-place finish, averaging 20 points per game.

After his senior year at Duke, Pocius represented Lithuania at the 2009 Summer Universiade in Belgrade, Serbia, where he led the team to a fifth-place finish, averaging 13.5 points, 5.8 rebounds and 1.3 assists.