The storm has caused several power outages and roads are closed throughout the county.
The Met Office has raised its weather warning to amber – with major disruption likely across the region.
Our photographer Brian Eyre has been out and about capturing photos and residents have submitted pictures of the flooding around Chesterfield.
Firefighters were called to significant flooding in the Goyt Side area of Chesterfield, specifically Chatsworth Road.
Members of the public were advised to avoid the area and asked not to cross Road Closed signs, or incident tape which may be warning of flooding in the area.
Specialist water rescue teams are working in the area to rescue stranded motorists and assist vulnerable residents. 20 residents have been rescued and evacuated by firefighters.
Area Manager Paul Moreland said: “Emergency services are dealing with significant flooding across the county with 20 residents being rescued from properties in the Goyt Side area of Chesterfield.
“The rescues that we have carried out in that area highlight the serious nature of the impact of Storm Babet and I need to ensure people listen to our warnings and follow our advice.”
1. The Riverside, Chesterfield
Deep water has flooded this area at the bottom of Hady Hill. Photo: Brian Eyre
2. Bottom of Hady Hill, Chesterfield
Derbyshire Times photographer Brian Eyre captured residents helping each other as the water rises in this part of Chesterfield. Photo: Brian Eyre
3. Grassmoor
Grassmoor has been badly hit with flooding. Chesterfield Road is currently underwater. Photo: Brian Eyre
4. Hasland
A van attempts to get through the deep water under the bridge. Photo: Brian Eyre