Although 4.5 million people could benefit, just 10,000 railcards are being offered on a first come, first served basis - meaning only about one in 500 people in this age range will have one.
The wait for the millennial railcard will soon be over, with another 10,000 going on sale today.
This railcard is only available digitally so you will need to download the Railcard app.
Others compared getting their hands on a railcard, to the elusive Golden Tickets in Roald Dahl's Charlie and the Chocolate Factory.
'Due to the unprecedented demand we have been working with our suppliers throughout the morning to further increase the capacity on the website to create a better experience for our customers. "Sort out your website to make it fair!"
Rail Delivery Group, the company that is releasing the millennial railcards, has yet to specify when they will be fully rolled out across the UK.
In a message to the National Railcards Twitter account at 7.48am, youth worker Josh Booth, from Leeds, posted: "Been trying to get 26-30 railcard since 7am, your website crashing and been on hold on the phone since then". "We're really sorry this is happing and have our whole team on it".
Tom Drury, from London, wrote: "The launch of the new railcard is a shambles".
The one year digital railcard costs £30 and provides a third off fares in England, Scotland and Wales.
The sale today, 13 March, is part of a trial extension that originally launched in December a year ago but was available only to customers using the Greater Anglia network.
Following the trial, only 10,000 are are initially being made available while the scheme is trialled to assess the impact on revenue and passenger numbers. A £12 minimum fare will also apply for journeys starting between 4.30am and 10am Monday to Friday, excluding advance fares.
'Research being gathered as part of the 26-30 Railcard trial expansion is being used to inform discussions with the government about a national roll out'.