The south-eastern coast of India has been hit by Cyclone Nilam, with wind speeds reaching 100km/h (60mph).
Nearly 4,000 people have been evacuated to escape the storm which is buffeting the city of Chennai. Several trees have been uprooted, but so far there have been no injuries.
At least 4,000 people in displacement camps in nearby Sri Lanka have been affected by flooding.
But the worst of the storm failed to hit Sri Lankan territory directly.
As it heads west, Cyclone Nilam is now hitting the Indian states of Tamil Nadu and Andhra Pradesh, and the town of Pondicherry.
Schools, colleges and cargo operations at the port in Chennai, Tamil Nadu's state capital, have been shut.
Fishermen in both states have also been warned not to venture out to sea.
India's weather department has warned of continual rainfall, strong winds and rising tides until at least Thursday morning.
It said in a statement that the storm had extensively damaged groundnut and maize crops, and thatched-roof properties, along the coast.
In addition power and communication lines have been put out of action.
The department has warned people living in the storm-hit areas to makes sure their escape routes are not flooded.
Authorities in the two states were put on alert ahead of the storm for at least 24 hours.
Reports say more than 300 schools and community centres in Chennai have been kept ready to receive evacuated people. Control rooms have opened in the vulnerable coastal districts of Andhra Pradesh.
Meanwhile, in Sri Lanka disruption was at its greatest in Mullaitivu in the north-east and Gampaha on the west coast. In the north, the Red Cross has been distributing tarpaulins, mats and mosquito nets. Strong winds and showers are still prevalent in the north and east.
The BBC's Charles Haviland in Colombo says that people in areas hit by heavy fighting at the conclusion of the war in 2009 have been badly affected.
In December 2011, more than 30 people died and many homes were damaged after a cyclone struck near Pondicherry.
And in May 2010 at least 23 people died as a powerful cyclone caused widespread havoc across Andhra Pradesh.