The heavy rains and tornado threats began Monday and were expected to continue through Wednesday, but local officials said the rain was dissipating Wednesday, RIA Novosti reported.
No emergency was declared in the city -- due to host the Winter Olympics in February -- the Emergencies Ministry said.
The rains caused miles-long traffic jams due to blocked roads and several flights at the city's airport were canceled, RIA Novosti reported.
Power company Kubanenergo said it cut off power to five regions in the city Tuesday to avoid electrical hazards and equipment damage that could have led to more widespread outages.
Swim Week Miami Beach 2014 [PHOTOS]