Hurricane Dolly has hit the Mexico-Texas coast, lashing the region with winds of up to 100mph (161km/h).
Dolly dumped about 12in (30cm) of rain over Texas before weakening from a category two to a category one storm, says the US national weather service.
Towns and cities in the Rio Grande Valley in southern Texas were put on alert in case the rain causes flooding.
Power cuts have left more than 12,000 customers without electricity, according to a Texas power company.
Earlier, residents were urged to move away from levees in case they were breached.
"Preparation to protect life and property should be rushed to completion," the National Hurricane Center (NHC) in Miami warned.
Storm surge
The leading edge of the storm reached Texas's South Padre Island before dawn, damaging the roof of an apartment building.
The causeway linking the island to the mainland had been closed earlier.
Storm's path
Forecasters have predicted Dolly would bring a coastal storm surge of up to 6ft (1.8m) above normal.
Based on Dolly's projected path, the US Census Bureau said that about 1.5 million Texans could feel the storm's effects.
Cari Lambrecht, a spokesman for Hidalgo County, Texas, said that shelters able to hold about 400 people have been opened.
She said they were encouraging people in low-lying areas to use the shelters.
"It's so much easier for them to go now instead of us having to pull them out later," she said.
Texas Governor Rick Perry has called up 1,200 National Guard members to help in any emergency caused by the hurricane.
In Mexico, Governor Eugenio Hernandez of the state of Tamaulipas, said officials planned to evacuate 23,000 people to government shelters in Matamoros, Soto La Marina and San Fernando.
In the Gulf of Mexico, Shell Oil evacuated workers from oil rigs, but said it did not expect production to be affected.