Some argue for a box shape while others argue for something that looked more like a ship.
And the recent discovery according to 4000-year-old Mesopotamian tablet (consisting of sixty lines in cuneiform) at British Museum saying that the Noah's Ark was round.
The 4000 year old clay tablet containing the story of the Ark and the flood stands on display at the British Museum in London during the launch of the book 'The Ark Before Noah' by Irving Finkel, curator in charge of cuneiform clay tablets at the British Museum.

Further more, some theorize it was a spaceship which could explain the rounded shape.
A spaceship would make more sense, as it would have been impossible to build an "Ark" or boat big enough to accommodate two of each species of living creatures on earth. And back then there was probably more different types of species compared to now after multiple extinctions.
Links:
- The Guardian: Noah's ark was round – so the ancient tablet tells us
- Daily Mail: Was Noah's Ark ROUND? 3,700-year-old clay tablet reveals giant boat was made out of reeds and bitumen
- Fox News: Ancient tablet reveals new details about Noah's Ark prototype
- Was Noah’s Ark Shaped Like a Box? by Bodie Hodge
- Yahoo Answers: Noah's Ark was a spaceship?