And low lying land and roads along the coastline are expected to be especially affected – with Powfoot on high alert.
The sea flooding will be a result of the high tides and prevailing bad weather conditions, say the council.
Meanwhile, Police Scotland is advising drivers locally to travel with caution today and tomorrow afternoon following the Met Office yellow weather warning for rain and strong winds across this region.
Inspector David Hynd said: “If you are driving a vehicle which may be vulnerable to being blown over in such conditions along exposed routes including bridges, please exercise additional caution and plan your route to avoid exposed areas or consider cancelling your journey until conditions improve.
“Previous incidents have clearly shown the dangers of driving vehicles vulnerable to being blown over in high wind conditions and the subsequent danger created for other road users, emergency services and recovery operatives where incidents have occurred due to drivers ignoring warnings.
“If you are travelling you should ensure you and your vehicle are adequately prepared for the conditions making sure you have sufficient fuel and supplies such as warm clothing, food and water in the event you are delayed for several hours. Charge your mobile phone and plan your route as well as alternative routes.”