Passengers travelling on the trains on the East Coast mainline are being told not to travel by train operating company LNER due to expected disruption caused by Storm Ciara.
LNER, who operate intercity routes between Edinburgh and London, Aberdeen and Inverness said speed restrictions imposed by Network Rail would lead to a "significantly reduced timetable" on Sunday 9 February.
The disruption could leave thousands of fans travelling to Edinburgh to watch England play Scotland at Murrayfield stranded in the Capital on Sunday.
The restriction, meaning trains will only run at 50mph, will mean cancellations, delays and significant disruption to services.
Customers have been told they can travel on Saturday 8 February before 6pm and on Monday 10 February if they wish.
Full refunds are also on offer if customers decide not to travel at all.
David Horne, managing director of LNER, said: “We are expecting significant disruption to LNER services this Sunday, so we are advising customers not to travel.
“Customers with tickets booked for Sunday should instead use their tickets to travel on any LNER service on Saturday 8 February, before 18:00, or on Monday 10 February.
“For customers who do not wish to travel, a full refund will be available without charge.”
A yellow weather warning for wind is in place for Edinburgh and the Lothians from 12pm to 23.59pm on Saturday 8 February, with a second wind warning in place from 12am to 23.59pm on Sunday 9 February.
The Met Office said: “Storm Ciara will bring very strong winds and potentially some disruption to travel throughout Sunday.”
A yellow warning for snow is also in place on Monday and Tuesday for Edinburgh and the Lothians.
The Met Office said: "Heavy snow and strong winds will combine to lead to disruption to travel, especially over higher routes.
"Frequent and heavy snow showers will affect the region throughout Monday and Tuesday. Snow showers will mainly be over high ground, giving slight accumulations of 1 to 3 cm above 150 metres and 5-10 cm above 300 metres.
"Snow will gradually build up and, in a few locations, accumulations of over 20 cm are possible by Tuesday evening over the highest routes.
"Strong winds, gusting 50-60 mph, will lead to blizzard conditions at times and considerable drifting of lying snow. Frequent lightning strikes are also possible, perhaps leading to interruptions to power supplies."