LNER says the thefts between York, Selby and Doncaster is causing disruption to journeys between these stations.
Services may be cancelled, delayed by up to 45 minutes or revised, a statement said.
A spokesman said: “We anticipate major disruption will continue until the end of the day. LNER are advising customers not to travel.
"Tickets for travel today will be valid for travel tomorrow.”
Buses have been arranged to run between York and Doncaster.
Passengers may also use tickets on:
CrossCountry between Sheffield and Newcastle / Edinburgh
Grand Central between Sunderland and London Kings Cross
Hull Trains between Doncaster and London Kings Cross
Northern between Carlisle and Newcastle
TransPennine Express between Manchester and Leeds / York / Newcastle
You can check your journey using the National Rail Enquiries real-time Journey Planner and can follow the incident on Twitter, please use #Doncaster