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The Dome is a gigantic glass dome placed over Springfield by the US Government and EPA. It is an almost impenetrable object that was put over Springfield due to it being the most polluted town in the World. It was a crisis so bad, it had its own name and theme music, Trappuccino.
The Dome could easily crush people when coming down, as one unfortunate person found out. It had to be transported by loads of helicopters with suction cups holding it up.
It could only be damaged after numerous repeated attacks. There would have been a way to destroy a hole with Professor Frink's Acid Shooting Ray. However, this was on the other side of the Dome. Repeated attacks, such as Stampy hitting it, could crack the Dome though. The Dome also had a massive television screen, invisible at first, that Russ Cargill, head of EPA, could communicate to Springfield on.
The Dome was finally destroyed by Homer and Bart on the day Springfield was to be blown to smithereens. Homer rode a motorcycle around the Dome with Bart throwing the bomb out of the hole on top (which was previously plugged up). The bomb destroyed the Dome, but not the town itself.
 Second dome
Mr. Burns brought in a second dome to cover Springfield with after everyone treated him horribly. He didn't go through with it after he was told that it had already been done before. Lou then states that they could always just dig out of it.