Train to and from Wakefield Westgate railway station are being delayed or cancelled.
East Coast has cancelled all services running in or out of London Kings Cross station and to or from Wakefield due to storm damage to overheard power lines, fallen trees and debris on the line.
Tickets for today will be valid for travel tomorrow.
Other services including Cross Country are also subject to delays and cancellations.
Services operating to and from Kirkgate railway station have not been affected as severely but passengers can expect slight delays.
Passengers have been advised to check www.nationalrail.co.uk for up to date information before heading to the station.