Aer Lingus today cancelled 20 flights to and from Irish airports to Scottish airports, while Ryanair cancelled some 36 flights, affecting two flights this morning between Dublin and Scotland.
The Irish Aviation Authority will announce early this afternoon if flights can resume, depending on the wind direction of ash clouds from the erupting Icelandic volcano.
Meanwhile, Ryanair said it carried out a one hour flight 41,000ft over Scotland this morning in the so-called "red zone" of the ash cloud from Glasgow Prestwick to Inverness, on to Aberdeen and then south to Edinburgh.
Aviation chiefs have deemed Scottish airspace "high ash concentration".
Ryanair said there was no visible volcanic ash cloud or any other presence of ash and post flight inspections revealed no evidence of ash on the airframe, wings or engines.
The low-cost carrier claimed the red zone was non-existent, mythical and a misguided invention by the UK Met Office and the Civil Aviation Authority (CAA).
Ryanair said it has written confirmation from both its airframe and engine manufacturers that it is safe to operate in the area.
"This morning's verification flight has demonstrated that the UK Met Office's 'red zone' forecasts are totally unreliable and unsupported by any evidence of volcanic ash concentrations whatsoever," Ryanair said.
Ryanair spokesperson Stephen McNamara said on Morning Ireland that they strongly objected to this decision and would be requesting a meeting with the IAA as soon as possible.
However Aer Lingus spokesman Declan Kearney said his airline had decided not to fly following consultation with their engine manufacturers.
Meanwhile, air passengers in Northern Ireland are also facing disruption this morning.
All of this morning's flights between Belfast International Airport and Edinburgh, Glasgow and Leeds-Bradford have been cancelled.
Iceland's most active volcano, Grimsvotn, started erupting on Saturday, sending a plume of white smoke miles high into the air.
Met Eireann meteorologist Pat Clarke stressed that weather conditions were markedly different this time to the last Icelandic eruption, with rapidly changing weather systems now, compared with a static situation last year.
The British Met Office, which has been monitoring the movement of millions of tonnes of ash still spewing out of Grimsvotn, said the whole of Scotland could be engulfed by a thick cloud of debris, while lower concentrations could affect airspace over northern England and Ireland.
Experts said the plume was drifting at a height of 20,000 to 33,000ft -- the normal altitude for passenger airliners -- and volcanic emissions could reach western France and northern Spanish airspace tomorrow if the eruption continued at its present rate.
Last year's eruption of the Eyjafjallajokull volcano brought the aviation industry in Europe to a virtual standstill.
One hundred thousand flights were cancelled, 10 million passengers were left stranded and the ash cloud cost the industry billions of euro.
The decision to order a blanket closure of European airspace was fiercely criticised by many airlines, who believed officials had overestimated the danger.
"I think the regulators are a bit more sensible than they were last year," said Michael O'Leary, chief executive of Ryanair.
"We would be cautiously optimistic that they won't balls it up again this year."
Philip Hammond, the UK's Transport Secretary, said the situation was being closely monitored.
"Clearly, this is a natural phenomenon that we cannot control, but the UK is now much better prepared to deal with an ash eruption than last year," he said.
Rochelle Turner, head of research for Which? Travel, said last year, airlines had been taken by surprise.
"Hopefully disruption will be minimal, but airlines will have no excuse if they fail to act quickly to inform passengers of delays and cancellations, or to provide the necessary assistance," she added.