Iarnród Éireann is warning passengers that they may face a second day of disruption tomorrow as a result of unofficial industrial action by train drivers.
Up to 35,000 rail users were affected today because of the dispute over the introduction of new trains.
Iarnród Éireann says the last train has left Heuston Station for the night with the 7pm train to Galway - five other scheduled trains for later tonight have been cancelled.
Of a total of 50 scheduled departures from Heuston Station today only 13 trains left the station.
Services to the west and south were disrupted by the action, which began at around 6.30am this morning.
Drivers are demanding reduced working hours if they are to operate new Mark Four trains, which were introduced on the Cork line today.
Iarnród Éireann earlier advised people not to travel by train unless it was absolutely necessary to do so, with passengers who needed to travel advised to contact the company.
The company's website, www.irishrail.ie, is carrying details of any changes in the company's services arising from today's industrial action.
The Taoiseach, Bertie Ahern, has said he is very disappointed at the drivers, particurlarly in the light of huge investment that the Government has made in Iarnród Éireann.
A small number of Inter City services left Heuston Station as scheduled this morning but the majority of services between Heuston and the south and west have been disrupted.
Iarnród Éireann has spent €117 million on 67 new carriages which it is hoped will hugely improve the frequency of its trains on the Dublin-Cork route by the end of the year.
The company had planned to introduce the first of those new trains on the route today for in-service training, but two drivers in Cork refused to operate the new trains.
The drivers have not been suspended but the company says it has told them they will not be paid until they operate the new trains.
A number of other drivers are now refusing to work in support of their colleagues.
Labour Court ruled against drivers
In January, the Labour Court ruled against drivers who were seeking a pay increase for operating the new trains.
Negotiations are continuing on other issues relating to extra money for agreeing to more stringent monitoring of driver standards and for coaching trainee drivers.
The company says it is committed to concluding an agreement on these issues but says they are not connected to the introduction of the new trains.
The drivers dispute this and say they cannot operate the new trains until an agreement has been concluded.
The drivers also say they have concerns about the training they received on the trains prior to their introduction to service.
