Behm, 33, underwent surgery Saturday night at Parkland Hospital in Dallas to repair a fracture of the thoracic spine and was listed in stable condition, the Cowboys said in a posting on their Web site.
Assistant athletic trainer Greg Gaither suffered a fracture to the tibia and fibula in his right leg, and like Behm, had surgery Saturday night. Gaither is expected to be discharged from the hospital this week.
"We are grateful that Greg Gaither's surgery was successful, and we feel blessed that others involved were able to walk away from this accident after receiving medical attention (Saturday) afternoon," team owner Jerry Jones said. "To the Behm family we extend our love, comfort, and the full support of every person and resource within the organization."
Special teams coach Joe DeCamillis was reported in stable condition and was expected to undergo surgery Monday to stabilize a fractured cervical vertebra, the team said. A total of 10 staffers were taken to area hospitals and there were two additional hospital walk-ins.
The storm, accompanied by 65 mph winds, hit about 3:30 p.m. CDT Saturday, toppling the air-supported roof of the eight-story facility on the second day of a rookie mini-camp at the Cowboys' training facility. The rookie mini-camp had been scheduled to end Sunday morning with a short practice, but that was canceled.
Instead, players attended a meeting Sunday before returning to either their schools or hometowns, the Cowboys said.