1. To run or rush out (of some place) all at once and in, or as if in, a wild panic. Nearly 30,000 people began stampeding out of the stadium at once as the fire began to spread. All the students stampeded out as the final bell of the school year began to ring.
2. To leave (some place) in very large numbers. During the economic recession, young people began stampeding out of the country in search of better opportunities elsewhere. Once it became clear that the hills had been stripped of their mineral deposits, all the prospectors and mining companies stampeded out all at once.