Eight flights between Ireland and London Heathrow have been cancelled because of severe weather. Aer Lingus services between Dublin, Cork, Belfast and Heathrow have been affected.
Also in the Republic, an orange 'Be Prepared' national warning is in place for gale force winds affecting all Irish coastal waters. A number of ferry crossing have been cancelled as a result.
Met Éireann predicted: "Southwest gales or strong gales at first this evening on coasts from Loop Head to Fair Head to Roches Point and on the Irish Sea.
"Northwest or cyclonic gale to storm force winds expected for a time tonight in the South Irish Sea.
"West to Northwest gales are expected to develop later tonight and tomorrow morning on all sea areas; with winds increasing to strong gale force at times tomorrow afternoon on coasts from Wicklow Head to Loop Head to Fair Head and on the South Irish Sea."
The Dublin City Marathon, which is scheduled to take place on Monday, is set to go ahead with a record number of participants.
Meanwhile, in England and Wales, a severe weather warning has been issued across a number of areas.
Wales, London, south-east and south-west England, the east and west Midlands, and the east of England are under an 'Amber' warning which means 'Be Prepared.'
The UK Met Office has given a lesser yellow warning, meaning "be aware", for the rest of Wales and England up to the border with Scotland.
Winds of more than 80mph are expected to bring down trees and causing widespread structural damage, leading to power cuts across a large part of the two countries.
The Met Office is also predicting that 20-40mm of rain could fall within six to nine hours overnight meaning surface water floods could strike much of England.
The storm has been named St Jude after the patron saint of lost causes, whose feast day is Monday.
It will develop over the Atlantic and is expected to hit the South West late on Sunday night, before moving north-eastwards across England and southern Wales.
Heavy rain will accompany it, with strong winds in the early hours of on Monday, but the storm is expected to have moved out over the North Sea by lunchtime, leaving strong breezes in its wake.
The Met Office described the storm as not one "you would see every year", and said the expected wind strengths would be similar to storms in March 2008, January 2007 and October 2000.
Frank Saunders, chief forecaster at the Met Office, said on Saturday night: "This is a developing situation and we'd advise people to stay up to date with our forecasts and warnings over the weekend, and be prepared to change their plans if necessary.
"We'll continue to work closely with authorities and emergency services to ensure they are aware of the expected conditions."
Atlantic storms of this type usually develop further west across the ocean, losing strength by the time they reach the UK and Ireland.
But this is expected to appear much closer to land, potentially moving across the country while in its most powerful phase.
A strong jet stream and warm air close to the UK are contributing to its development and strength.
The Environment Agency has teams working to minimise river flood risk, clearing debris from streams and unblocking culverts, and are closely monitoring water levels so they are ready to issue flood warnings if necessary.
A spokesman said: "We are supporting local authorities who will respond to any reports of surface water flooding.
"Seafronts, quaysides and jetties should be avoided due to the risk of overtopping by waves and wind-blown shingle."