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
More than 15 people are dead and 20 remain missing after Hurricane Maria's direct hit on Dominica, the prime minister has said.
The long-time host of one of TV's toughest quizzes found love on the show, produced several TV hits and helped lead a historical campaign.
Donald Trump has announced a new order to help the US target people, and organisations financing and facilitating trade with North Korea.