The Scottish Environment Protection Agency (Sepa) has issued 12 flood warnings and eight flood alerts.
Some areas have also been marked for flood alerts where flooding is possible.
Sepa hydrology manager Marc Becker said: "We would encourage people in the areas potentially at risk to remain vigilant and be mindful of the conditions in their locality and when travelling.
More top news
Mild air but windy & wild
House of Cards actor Kevin Spacey is understood to be being investigated by British police over a second alleged sexual assault.
The biggish politics from the Budget is that there will be a £6bn stimulus in the year before Brexit and £10bn in the year after Brexit.