An Armagh Post Office gave out 400 Irish passport forms on Friday.
The huge surge was witnessed at the main Post Office in Emerson’s Supermarket on Scotch Street.
There were reports of Post Offices across the Province being left with no forms such was the demand.
It came after Friday morning’s confirmation that the UK had voted to Leave the EU – despite both Northern Ireland and Scotland voting to remain.
The Post Office at Scotch Street would normally have issued about 30 forms in a day.
It was the biggest ever demand for Irish passport forms witnessed in Armagh since the Post Office transferred there.
And it would seem to be a pattern which is not going to be letting up any time soon.
On Friday, a local SDLP councillor urged County Armagh residents who wanted to apply for Irish passports to act fast.
Councillor Sharon Haughey-Grimley said she had been receiving a lot of enquiries from the public in the wake of the EU Referendum.
In Newry and Armagh, 31,963 voted Remain and 18,659 Leave, with 22 votes rejected.
The fall-out is currently being debated in the Assembly.
Councillor Haughey-Grimley has assured people that those in Northern Ireland are “entitled to dual citizenship as enshrined in the Good Friday Agreement and British Irish Agreement of 1998”.
And, speaking on Friday, she added: “It is also a matter for the Irish Government to determine who is eligible for an Irish passport.
“In a nutshell, yes people in Northern Ireland can still apply for Irish passport at the minute and it looks like there’s going to be huge number of applications submitted over the coming days and months which will undoubtedly lead to delays.
“I and other SDLP elected representatives can sign forms which are available in SDLP Armagh and Newry Offices and at Post Offices.”