Law and politics student Luke Mac an Bháird said the crowd at Gate B at Brussels Airport were evacuated to the back of the terminal after the two separate explosions.
The crowd were first told to remain put, before they were evacuated to a tarmac area at the back of the terminal.
He described how a stampede began as panic set in.
"I was at Gate D when it happened. I was listening to music, I didn't actually hear the explosion but there was a lot of panic and people running with their children.
"There was just a mass of people at once running to the bottom of the gates, they were saying that another bomb was coming," he told the Anton Savage Show on TodayFM.
"I didn't know what was going on. It was very confusing."
Mr Mac An Bháird described scenes of panic in the airport as people were evacuated.
"They've put us on a bus and [parked] at the side of the runway. They've evacuated everyone to the tarmac in the last hour or so.
"When they were moving us from the gate to the tarmac on the runway, there was hundreds of people queued up at the tunnel as if they were going to [board a plane] but we were going out through an exit door.
"People started to scream and run again and there was a bit of a stampede towards the tarmac.
"Fortunately I didn't see any injuries... I went straight through security to wait for my flight but there was a lot of hysteria. It was quite a scary moment.
The Erasmus student said that the response from airport officials was "immediate".
"Ever since what happened in Paris last year, there's always an army presence [in Brussells]. Even this morning when I got the train to go to the airport the army was there but there was nothing different today though to suggest that something was [about to happen].
"What really put it into perspective for me was hearing thousands of people shouting all at once," he said.
"It was very surreal... it was like everything was going in slow motion for the first ten seconds."
Mr Mac An Bháird has said that the passengers waiting on the runway have not been advised on where they will be transported to.
"There's been no information about where we will be transported to. There's about six or seven ambulances coming in right now."
Speaking to Sky News, Mr Mac an Bháird said; "There was about 100, 150 people there and we were told there was a bomb going off in the airport. People were quite scared and there were a load of people crying.
"There was very little being said to us only to run to the back.