In the city of Orsk alone, where more than 200,000 people live, 4500 houses were underwater.
Videos and pictures showed that in some places only the roofs of buildings were protruding above the water.
A state of emergency has been declared in the region.
The city of Orsk was hardest hit with more than 4500 houses inundated and thousands evacuated. (EPA PHOTO)
Civil Defence Minister Alexander Kurenkov described it as a "critical situation" on Sunday as he visited Orsk.
More than 4000 people had been brought to safety, while 11 emergency shelters had been set up for more than 8000 people.
Four deaths were reported in Orsk, but according to authorities these were not related to the flooding.
Orsk is located around 1700km southeast of the capital Moscow and close to the border with Kazakhstan.
The first dam burst on Friday, and the second on Saturday, as the waters coming down from the mountains increased the pressure on the barriers.
The water levels are expected to rise even further due to rainfall.
About 1600 properties were flooded in the regional capital Orenburg.
The public prosecutor's office has initiated criminal proceedings for negligence in the wake of the flooding, possibly related to an inspection of a dam in 2020 which identified 38 defects and ordered them to be rectified. It was unclear whether the problems had been fixed.
The mayor of Orsk said last week during a visit to the site that the dam was robust.
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