The Met Office has amber “be prepared” warnings for Moray, Aberdeenshire, Angus, Perthshire and Stirlingshire.
The Scottish Environment Protection Agency (Sepa) has issued about 30 flood warnings.
The warnings, which mean flooding is expected, are mostly for the Tayside, Angus, and Dundee areas, as well as Aberdeen and Ballater in Aberdeenshire.
Sepa has now added the Scottish Borders to its list of alerts, where flooding is possible, bringing the number of alerts to four.
They come as Scotland continues to clean up after Storm Frank hit on Wednesday.