They cover Grampian, Tayside, central Scotland and Fife until Monday night.
The Scottish Environment Protection Agency has issued more than 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.
Vincent Fitzsimons, Sepa`s hydrology duty manager, said: "Rivers have been rising since Saturday and flood warnings have been issued.
"It`s important to note that the rain is less intense but more prolonged than during Storm Frank.
"This means that rivers will rise more slowly but then stay high for much longer - from Sunday through till Tuesday. The peak for most areas will be on Sunday night and Monday morning."
Mr Fitzsimons said river levels in the north east were of most concern, including those around Kintore, Inverurie, Brechin and Aberdeen, but the agency was also keeping a close eye on communities in the Borders and Caithness.
River levels in parts of Angus are predicted to peak late on Monday morning to a similar level to which they did during Storm Frank.
Angus Council said residents beside the River South Esk in Brechin should put door guards and sand bags in place and said there was the potential for surface water issues behind the new flood protection which is currently under construction.
A Met Office spokesman said: "Over the period ending late Monday, many areas look like receiving a further 40-80 mm of rain, with some of the high ground receiving 100-150 mm - this in addition to that which has fallen over the previous 24 hours.
"However, this looks like being fairly evenly spread out, which should slightly ease the resulting impacts.
"Given the saturated nature of the ground, there is a greater risk of surface water and river flooding than might normally be expected."
Insp Simon Reid said: "We would ask the public to be mindful of road closures. "If roads are closed they are closed for a reason. They are there for safety. Please be sensible, adhere to them and don`t put yourselves or others at risk."
A cable damaged by Storm Frank led to the loss of the telephone service, including 999 calls, in Braemar and Crathie.
Work has been carried out to repair the cable and BT and the Red Cross have provided temporary cover through communication vehicles in those areas.
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