Latest travel update: Delays expected over coming days
Dublin Airport was expecting 28 flights out of the city to be cancelled today and more than 48 cancellations of flights into Ireland.
Cork Airport said at least five flights had been cancelled and it expected its first arrivals after 4pm.
Shannon, which welcomed the first transatlantic service into the country last night, said it expected eight arrivals to be cancelled but urged passengers to contact airlines to check if departures were going ahead.
Ryanair said it was cancelling flights on services between Ireland and the UK until 5am on Friday to free up aircraft to clear passenger backlogs across Europe.
The airline said southbound flights from Spain, southern Italy, southern France, Malta and Morocco were operating as normal while flights across the north of the continent will operate from 5am tomorrow.
Chief executive Michael O'Leary warned there will be considerable air traffic control and airport delays over the next few days due to intense demand for flights.
"We have issued instructions to all of our airports that our immediate priority will be to ensure that no seat operates empty, while there are backlogs of disrupted passengers wishing to travel," he said.
"Accordingly Ryanair will be operating extra flights on those routes where we believe there are significant numbers of disrupted passengers."
Ryanair has come under fire after warning it will only offer passengers reimbursement for expenses incurred during the six day grounding based on the air fare they originally paid.
Authorities have insisted the airline must abide by European rules to meet passengers` costs and urged people left out of pocket to pursue claims.
"While we will consider all passenger requests for reimbursement of reasonable receipted expenses over the past week, any such reimbursement will be limited - as it is in the case of rail, coach and ferry passengers - to the original air fare paid by each passenger," Mr O`Leary said.