Environment Agency (EA) has issued 17 flood warnings and five flood alerts for the city, with bus services being diverted, train services being cancelled and major roads being closed.
The EA said that its incident response crew is keeping a careful eye on the forecast on a 24-hour basis.
Here are some of the pictures captured around Sheffield after the rain started to fall on Sunday morning.
1. Meadowhall
Meadowhall bosses say its flood defences have been deployed as a precautionary measure but the centre remains open. Photo: Dean Atkins
2. Meadowhall
Rising water near Meadowhall has forced Meadowhall Road to close. Photo: Dean Atkins
3. Meadowhall
Water rising rapidly at the River Don Photo: Dean Atkins
4. Coronation Park, Oughtibridge
The floodwater has also overflowed to Oughtibridge Sports Club, which is located next to Beeley Woods and the river. Photo: Matt Dixon