Red Cross spokeswoman Anita Foster says no injuries were immediately reported in high winds and heavy rain in the Dallas-Fort Worth areas.
Shelters were set up at a church in the Johnson County town of Lillian, and in Tarrant County, in Hurst, at a convention center, according to Foster.
One hangar at Addison Airport, in the Dallas area, lost part of its roof.
Some 3,300 customers were without power in the Dallas-Fort Worth area. Another 1,000 were without power in the West Texas city of Breckenridge, said Megan Wright, a spokeswoman for Oncor Electric Delivery. It's unclear how long it will take to restore power.
The storms have caused frequent lighting and wind gusts of up to 80 mph in some areas. They carried embedded tornadoes and prompted a series of tornado and severe thunderstorms warnings throughout North Texas early Thursday, said Tara Dudzyk, a meteorologist with the National Weather Service in Fort Worth.
The storm also brought heavy rains flooded roads making it difficult for drivers to get around, reports CBS News' Early Show Weatherman Dave Price. Winds were powerful enough to tear apart trailer homes and flip a local oil rig right on to its side.
The system continued moving quickly, heading toward East Texas, Dudzyk said.
An apparent tornado packing winds of up to 70 mph moved through West Texas after midnight Thursday, tearing shingles from roofs, shattering glass and flipping over vehicles.
Paramedics were dispatched throughout the city, but San Angelo police didn't have a number of injured.
The storm pelted the city with quarter-sized hail. At least one building downtown was damaged and power lines were down in some areas, said Hector Guerrero, a meteorologist with the National Weather Service in San Angelo.
Hours earlier, two apparent tornadoes also moved through another section of West Texas, sending three people to a hospital, destroying hangars and other buildings at a town's airport and knocking out power.
National Weather Service staff planned to survey the areas later Thursday to confirm if tornadoes touched down.
Police in the Stephens County city of Breckenridge said they have reports of a few minor injuries, but didn't have a full count by Wednesday night. Robbie Dewberry, administrator at Stephens Memorial Hospital, said the three were being treated in the hospital emergency room.
Price reports the storm has killed at least one person, injured 15 others and destroyed half a dozen homes.
The hospital was on emergency backup power. No damage was reported at the facility, Dewberry said.
Power lines were down and at least five homes were destroyed in Breckenridge, police said.
Another tornado apparently touched down in Palo Pinto County between Graford and Oran, said Jennifer Dunn, a National Weather Service meteorologist. Officials reported roofs were blown off a few homes and trees were down in Oran.
A tornado was also spotted in Hanna, Okla., ripping roofs off and scattering debris. High winds overnight may have damaged as many as 500 homes, reports Price.