Damage has been caused to overhead electric wires at Hest Bank, meaning all lines are blocked between Lancaster and Carlisle.
Trains on this route may be delayed by up to 60 minutes or cancelled, according to Network Rail.
Buses will now be run between Preston and Carlisle.
Passengers also face disruption between Lancaster and Oxenholme Lake District and Windermere, which is expected until 6pm today, January 16.
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Trains are also unable to run between Preston and Carnforth, with buses being provided instead.
Trains from Manchester to Barrow will run as far as Preston.
Trains from Barrow towards Manchester will run as far as Carnforth.
For more information see HERE.