Hurricane Sandy has strengthened into a strong category two storm as it makes landfall in south-east Cuba.
It hit maximum sustained winds of 175 km/h as it hit land just west of Santiago de Cuba, the BBC reports.
One forecaster says it could get bigger as it heads to the Bahamas and later Florida.
At least one person died as Sandy earlier swept over Jamaica, where power has been cut to most areas.
Local television reported 73% of the island has been left without electricity after strong winds and heavy rainfall brought down trees and power lines.
Curfews remain in place to prevent looting, and the BBC reports the initial fatality was a man crushed to death by boulders as the one hurricane - then rated as at category one - struck the island on Wednesday, unleashing heavy rains and winds of 125 km/h.
The elderly man was hit by by stones that fell from a hillside as he tried to get into his house in a rural village, authorities said.
Schools and airports are closed, and a curfew has been imposed in major towns. A police officer was shot and injured by looters in the capital, Kingston.
Moving across the islands at 22 km/h, the hurricane struck Kingston on Wednesday evening and headed north, emerging off the island's northern coast near the town of Port Antonio.
"It's a big storm and it's going to grow in size," said forecaster Michael Brennan from the National Hurricane Center (NHC) in Miami.
The NHC predicts that Sandy could dump up to 50cm of rain across parts of Jamaica, Haiti, the Dominican Republic and eastern Cuba.
"These rains may produce life-threatening flash floods and mudslides, especially in areas of mountainous terrain," the centre warned in a statement.
More than 1000 Jamaicans sought refuge in shelters, with residents reporting widespread power outages, flooded streets and damages to buildings.
Much of the island's infrastructure is in a poor state of repair, and a lack of effective planning regulation has resulted in homes being built close to embankments and gullies.
The country's sole energy provider, the Jamaica Public Service Company, said 70% of its customers were without electricity.
In some southern Jamaican towns, crocodiles were caught in rushing floodwaters, which carried them out of mangrove thickets, the Associated Press reports.
One big crocodile was washed into a family's front yard in the city of Portmore.
While Jamaica was ravaged by winds from Hurricane Ivan in 2004, the eye of a hurricane hasn't crossed the island since Hurricane Gilbert in 1988.
Almost 50 people were killed by that storm, and the then Prime Minister, Edward Seaga, described the hardest hit areas near where Gilbert made landfall as looking "like Hiroshima after the atom bomb".