There were fears of widespread disruption after the Dublin-based carrier lost a High Court bid to force its pilots to take to the skies.
But the airline reported a 97 per cent punctuality rate for its first departures and arrivals at UK airports today, blaming the small number of delays on air traffic control issues.
Ryanair said: "We do not expect any disruptions to our flights to or from our UK airports today.
"We wish to thank all our UK pilots who have chosen to work to protect the flights and travel plans of our customers and their families over the bank holiday weekend."
A judge sitting in London on Wednesday rejected an urgent application by the airline for an injunction against the British Airline Pilots' Association (Balpa).
Following its court victory, Balpa said it had offered to reopen talks with Ryanair in a last-ditch attempt to avoid industrial action in a dispute over pay and conditions.
But the union said the airline had "rejected the offer out of hand" and the strikes would go ahead as planned from 12:01am on Thursday to 11:59pm on Friday.
Balpa general secretary Brian Strutton said: "We are extremely disappointed that Ryanair have taken such a belligerent and negative stance.
"We have become used to their macho posturing but sadly it is their passengers who will pay the price for Ryanair's attitude."
A second round of strikes is planned between 2-4 September.
Just a few hours before the judgment in London, Ryanair won a similar legal move at the High Court in Dublin, meaning flights departing from Irish airports are operating as normal.
The airline urged the Forsa union and what it described as "this small minority of very well paid Irish pilots" to resume mediation.