There has been huge disruption on the network due to damage to their electric trains.
The live travel updates on their website is showing delays of up to six hours on some services.
-> More than six miles of delays on M62 near Leeds after crashTickets date for Tuesday April 16 will be valid on Wednesday April 17.
A statement on the LNER website said: "Due to severe disruption on the LNER route, we're advising customers not to travel today.
"This disruption is being caused due to damage to our electric trains, the cause of this is being investigated by our engineering teams and Network Rail.
"Your tickets dated for travel today, Tuesday 16th April, will be valid for travel tomorrow, Wednesday 17th April. If you're not able to travel tomorrow, you'll be entitled to a refund.
-> Train delays coming into Leeds after person found dead on tracks at Brighouse"We’re doing everything we can to get services up and running again and we're sorry for any disruption to your journey today."
It follows a morning of severe traffic disruption across West Yorkshire, with delays on trains around Brighouse due to a body on the tracks and a crash on the M62 causing tailbacks of six miles.