Here are the latest developments in this big story:
The Met department has forecast rain over the next three days with the next 48 hours being very critical. "The phenomenon will continue for the next seven days, but the next 48 hours are very crucial. Neighbouring states will also see rainfall activity," LS Rathore, Director General of Indian Meteorological Department told reporters in Delhi. It is the worst rain in Tamil Nadu in nearly 100 years.
The water level has been rising in parts of the city. The Saidapet bridge over the Adyar river, which runs through the city, was closed to traffic as water spilled on to the road.
After heavy rain for weeks, the runway at the Chennai airport is flooded and all flights have been cancelled. At least 50 trains have been cancelled.
Prime Minister Narendra Modi this morning held a meeting with senior ministers Arun Jaitley, Rajnath Singh, Sushma Swaraj and Venkaiah Naidu on the situation in Chennai. A discussion is being held in the Lok Sabha.
Telecom Minister Ravi Shankar Prasad has said that state-run operator BSNL will not charge anything for a week in Chennai. He also said that there will be no non-payment disconnections till the end of December.
The Army, the Navy, the Air Force and the National Disaster Response Force are out on the streets to rescue people from their flooded homes. The Army has rescued over 2000 people today. "We have never seen so much rain and destruction in Chennai," said Union Minister of State for Home, Kiren Rijiju.
Residents were seen climbing out of their homes or being pulled out to safety in the low-lying parts of Chennai where water is almost neck-deep. SOS messages on social media have led to rescues from buses, cars and rooftops.
Schools have been forced to close and exams have been postponed at least for this week. University exams have also been postponed.
In many parts of Chennai, residents have opened their doors to strangers, offering food, shelter and even mobile recharges. Malls, cinema theatres and offices opened their doors to stranded people.
Power supply in the city is very erratic. There has been no power in IIT-Madras since yesterday. People are stuck in many areas without food or water.
The Chennai Corporation has announced Emergency Contact Numbers for all the regional zones in the city. People can contact the following numbers in case of any emergency due to the floods.
Emergency Toll Free Number: 1910, State Emergency: 1070, District Emergency: 1077, Electricity:1912, Fire & Rescue: 101, Ambulance: 108, Tree fall, waterlogging - 1913, Sewage overflow - 45674567, 22200335
Helpline Numbers: Tiruvottiyur : 09445190001, Manali: 09445190002; Madhavaram: 9445190003, Ambattur: 9445190007; Tondiarpet: 9445190004, Royapuram: 9445190005; Annanagar: 9445190008, Teynampet: 9445190009, Alandur: 9445190012, Adyar: 9445190013,Perungudi: 9445190014
Flood Control Room: 28593990, 044-28410577,9445869843/47