Does the universe have a shape?
In short, no.
The universe doesn't have a defined shape for several reasons, however, it does have a general shape it resembles. The universe is round for the most part but not all angles are equally full so to say. There is a so called "center" and this is where the Big Bang occurred. After this event, all of the matter in the known universe was spread in a mostly even fashion at a particular speed outwards. This speed is constantly slowing however as gravity is causing the universe towards a possible "Big Crunch," where all matter will be brought back into an infinitely small point.
This means that the universe is mostly round, but has no true shape.