Three people were killed in the storm in Ireland, while around 245,000 homes were left without electricity. In Northern Ireland some 3,600 were without power before the storm then moved onto Scotland.
In a statement on its website BA said: “Due to strong winds forecast for Tuesday, we are giving customers travelling to or from Dublin or Belfast on Tuesday the option to move their travel dates.
“Customers travelling to or from Aberdeen, Edinburgh, Glasgow, Inverness, Isle of Man, Leeds-Bradford, Manchester or Newcastle on Tuesday can also opt to change their travel dates.”
The airline added: “We expect at times that the winds may be too strong to safely operate loading and unloading vehicles at some UK airports, so some flights are likely to experience delays.”
EasyJet said strong winds from the storm had also impacted its flights to and from Belfast as well as the Isle of Man on Monday.
It added that it was still operating its flights as scheduled “but there may be some delays throughout our network” for flights today.
Meanwhile Flybe said it had been forced to cancel some 170 flights due to Storm Ophelia, which swept across the UK and Ireland yesterday.
The airline also said it was offering customers the option to rebook flights on Tuesday.
Flybe said it had cancelled flights to and from Belfast City Airport and the Channel Islands, as well as the majority of its flights to and from Southampton.