Richard Broadbent said his partner and daughter were due to fly to Newcastle at about 19:00 but were stuck at the airport.
“She said suddenly all flights were cancelled and all passengers were moved to one place down at ground level, and it was absolutely packed.
“Then alarms started going off, people were screaming and passengers were trying to break out, there was no staff,” he said.
“She was ever so upset, I could hear people screaming on the phone.”
A Bristol Airport spokesperson said: “Due to a defect on the runway, we have temporarily suspended operations as a precaution, in order to inspect and repair the section affected.
“We apologise for any inconvenience. Safety is always our number one priority,” they added.
“Customers should refer to their airlines with any flight queries.”