TransPennine Express (TPE) asked customers to plan carefully as there will be an amended timetable in place because of the action by members of the Rail, Maritime and Transport union (RMT).
“We’re advising customers not to travel on the majority of routes and to plan carefully if journeys are necessary,” said the company.
Services affected on Sunday will hit routes around Liverpool, Manchester, Lancaster, Carlisle, Leeds, Hull, York, Scarborough, Middlesbrough, Newcastle and Edinburgh via Huddersfield.
The RMT has also announced further strikes on Sundays until June 5, on Easter Saturday, April 30 and on June 4, the Jubilee Bank Holiday.
The union said there is a large discrepancy in pay levels for conductors and other train crews for doing the same thing.
General Secretary Mick Lynch said: “Our rock solid strikes will bring the network to a complete standstill and the blame firmly lies with TPE management’s intransigence on this issue.
“What we are asking for would cost the company less than the loss of revenue from strike action.
“RMT remains open to talks about properly rewarding our conductors for the crucial role they play in keeping the trains moving.”