At least 41 people were taken to area hospitals. Dr. Paul Pepe, medical director for the Irving Fire Department, said at least three of the patients were in critical condition, CNN reported.
The bus -- operated by Cardinal Coach Line, based in Mansfield, Texas -- was carrying a group of people, mostly in their 60s, 70s and 80s, to Choctaw Casino in Oklahoma when it overturned on northbound State Highway 161 and Belt Line Road, The Dallas Morning News reported.
One of the four missing passengers is "Casino" Sue Taylor, 81, one of the organizers of the trip, the newspaper said.
Her daughter, Marsha Taylor, 56, said she has been told her mother is not one of the two people confirmed killed in the crash.
A passenger on the bus said it appeared the vehicle went out of control after a tire blew out.
"We ended up swirling and weaving and then ended up on the side," Daniel Risik told the newspaper. "People were screaming and hollering, a very traumatic situation to say the least."
Risik said most of the passengers weren't wearing seat belts and were thrown around the bus.
The Texas Department of Public Safety confirmed the two deaths, the newspaper said. The names of the dead have not been reported.
The injured were taken to Baylor University Medical Center at Dallas, Parkland Memorial Hospital and Methodist Dallas Medical Center.
The National Transportation Safety Board has sent investigators to the scene.