The first two trains sold out within minutes and, when a third train was put online yesterday, the Translink website appeared to crash.
Translink Twitter account said: “We are experiencing issues with our website at present.
“We are working to to resolve it. We’ll provide an update as soon as we can. Apologies for any inconvenience this may cause.”
A huge contingent of Armagh fans are expected to travel to Dublin on Sunday for the double header in Croke Park.
A Translink spokesperson said: “We are running three train specials to the Armagh v Galway GAA All-Ireland quarter final at Croke Park on Sunday 26th June.
“The first two trains, from Belfast to Dublin, sold out within minutes of tickets becoming available last week and the third train, from Portadown to Dublin, sold out yesterday afternoon.”