ScotRail said more than a month’s worth of rain is expected to fall in many areas across eastern Scotland between Thursday and 7am on Saturday.
The Met Office has issued a yellow weather warning of rain for eastern Scotland, which is in force from 3pm on Thursday until 6pm on Friday.
An amber “heavy rain” weather warning is in force for Aberdeen, Aberdeenshire, Angus and Perth and Kinross from midnight on Thursday until 3pm on Friday.
The yellow alert warns of rainfall building up across the high ground of eastern Scotland, with 50mm to 70mm expected, and up to 100mm possible across the hills of Angus and Aberdeenshire.
Forecasters said the area covered by the amber warning could see more than 100mm of rain, and even 150mm in parts of the Grampians and Cairngorms.
The Met Office warned there could be a danger to life in parts of eastern Scotland.
Network Rail Scotland said it would impose speed restrictions on some routes for safety reasons from Thursday afternoon “due to the extreme rainfall that’s been forecast”.
Journey times on those services will take longer.
Parts of the Edinburgh to Aberdeen, Stirling to Dundee and Ladybank to Perth routes will be affected, as will part of the Highland Main Line and the East Coast Main Line between Edinburgh Waverley and Berwick.
ScotRail tweeted on Thursday morning: “Over a month’s worth of rain is expected to fall in many areas across Eastern Scotland between now and 0700 on Saturday.
“For your safety, speed restrictions will come into place later today – check your journey on our app before travelling over the next few days.
“The first route to be affected will be Edinburgh-Dunbar in both directions from 1200 today.
“Trains will be limited to 40mph (down from 100mph) over a seven-mile section of track, adding around 10 minutes to journeys.”
The Met Office yellow warning covers Central, Tayside and Fife, Grampian, Edinburgh, the Lothians and the Scottish Borders, as well as Northumberland in north east England.
Craig Snell, from the Met Office, told the BBC: "The warning areas are where we are most concerned about the risk of flooding, but it doesn't mean that the areas outside them are not going to see some pretty atrocious conditions."
Scotland could see "two days of persistent rain", Mr Snell said, and this may result in snow additionally falling in the Scottish Highlands.
The Met Office yellow rain warning remained in place on Thursday for an area stretching from Birmingham, Lincoln and Hull to north Wales, Liverpool and Manchester.
Elsewhere, the M23 was closed in both directions between Junction 10 for Crawley and Junction 11 for Pease Pottage, both in West Sussex, due to standing water on the carriageway in the early hours of Thursday morning.
Flooding between Lewes and Brighton stations also caused disruption to Southern services on Thursday morning.