The Met Office has put flood warnings in place for Tayside, Ayrshire, West Central Scotland, Dumfries and Galloway and the Borders.
The Whitesands area in Dumfries has flooded after the River Nith burst its banks.
Police Scotland said road closures in the town had caused traffic to become gridlocked, while around 25 riverside homes have been evacuated.
Water levels were being closely monitored on a number of other rivers in the region, including the Cree in Newton Stewart.
Police Scotland also highlighted further road closures in the region, including the A701 road at Hidden Corner on the outskirts of Moffat, the A7 road to the south of Langholm, between Skippers Bridge and Middleholm, the A762 at junction with A713, north of Castle Douglas, and the A75 road at Daiseyknowe, Glenluce.
Meanwhile a number of homes have also been evacuated in New Cumnock, Ayrshire, due to flooding.
The Met Office also has flood alerts in place for Edinburgh and the Lothians, Aberdeenshire, Dundee and Angus, Argyll and Bute and central Scotland, indicating that flooding in these areas is possible, and people should be prepared.
Drivers are advised to check their intended route with www.trafficscotland.org before setting off on a journey.
Scottish Fire and Rescue Service said its crew are attending flooding incidents in Penicuik and East Calder in the Lothians, and at Cherrybank Inn in Perth.