The effect of storms on ageing trains means an “unprecedented” third of the fleet of 127 are damaged, so many will not run or be replaced by buses.
Transport for Wales (TfW) said they were trying to “share the pain” by diverting trains from quieter to more popular services.
But it has warned passengers face cancellations and busier trains.
TfW director of customer services, Bethan Jelfs, said: “Customers are affected throughout our network.
“We are really sorry this is impacting on customers and their journeys and day to day lives.
“We are trying to share that pain around and trying to run trains where the need is greatest, but pretty much all of our routes will be affected.”
Train users can find the latest travel news on the TfW live update website.
Services between Cardiff and Carmarthen, Swansea and Fishguard, the Cambrian line between Aberystwyth and Shrewsbury and Heart of Wales line from Llanelli to Llandovery are all affected.
Valley trains into Cardiff and between Llandudno Junction and Blaenau Ffestiniog will also be reduced.
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“There are some replacement road transport provision in place for customers and that really is regrettable because we’re not able to run the level of service we want,” added Ms Jelfs.
“We are running services as much as we can but some will be short-form, so customers may experience trains busier than usual.”
Fans travelling to and from Cardiff for Saturday’s rugby union international at the Principality Stadium between Wales and South Africa were also hit.
However the problems are set to worsen as commuters take to the network.
TfW, who took over the £5bn franchise from Arriva Trains Wales in October, said 37 of their 127 engines were currently out of service.
They blamed damage to wheels on the seasonal conditions, including Storm Callum, and said engineers were working ’round the clock’ to get engines back on the track.
Some rail users have taken to social media over the past few days to express their frustration.