Northern said services across its whole network could be cancelled, delayed or revised due to flooding. The disruption is expected to last all day on Saturday (November 9) and possibly into Sunday.
Passengers are advised to make alternative arrangements if travelling from Rotherham, due to severe flooding at Rotherham Centrall, Moorthorpe and Conisbrough. Services between Sheffield and Leeds and Sheffield and Doncaster have been suspended until further notice.
Services between Doncaster and Scunthorpe and Hull and Sheffield have also been badly affected, and passengers are either advised to not travel or make other arrangements. No road replacement services are in place on these services due to road closures also caused by the flooding.
The Hope Valley line, trains between Sheffield and Leeds, and Gainsborough/Lincoln to Sheffield are all now scheduled to run but may be subject to some delays.
A Northern spokesperson said: "We are still experiencing disruption on some routes in South Yorkshire and this is likely to continue into the weekend.
"We are still advising customers on these routes not to travel as flooding is making rail and road travel extremely difficult.
"Colleagues at Network Rail have inspected the tracks and working hard to return them to normal working, but at present we have no estimate as to when we will be able to operate services on the affected routes."
The spokesperson added: "Northern would like to thank customers for their understanding and patience as we continue to try to run as many services as possible."