The rail company said an embankment beneath the railway was significantly damaged during extreme weather on December 30 and requires “extensive work to stabilise and repair the foundations of the tracks to allow the railway to safely reopen”.
It said engineers are working to remove landslip material on a 40m-long section of the line and reinforcing it with more than 200 tonnes of new stone.
They will then relay the track above and check signalling systems, which they said will take several days to complete.
A Network Rail spokesperson said: “Flooding has caused significant damage beneath the track and we will need to rebuild the supporting embankment before re-opening the line.
“This is a very challenging project, but we understand the inconvenience closing the line will cause to customers and are working hard to reopen the railway as quickly as we can.”
An Avanti West Coast spokesperson said: “While our colleagues at Network Rail are working hard to reopen the affected parts of the line damaged by the landslip caused by extreme weather, our advice to customers is do not to travel to and from Scotland on the West Coast Mainline.
“Customers are being advised not to travel north of Carlisle as there are no services. An amended timetable is in place between Carlisle and London Euston.
“Customers travelling south of Carlisle are being strongly advised to check their journey before they travel. We thank our customers for their patience in what are very challenging circumstances.
“If you are no longer able to travel, you can claim a full fee-free refund from where you bought your ticket. For further travel information on please visit www.avantiwestcoast.co.uk.”
Passengers planning to travel between Glasgow/Edinburgh and Carlisle should check their journey before travelling with Network Rail or with their individual train operator.