The patrol says the 55-year-old pilot, Randall Lee Harris, and 25-year-old 1st Lt. Dale Bryan Shillington were pronounced dead at the scene. Shillington was posted at Vance Air Force Base in Enid.
No one on the ground was injured.
The patrol says Harris, of Owasso, Oklahoma, attempted an aerobatic maneuver, but lost control of the aircraft and was unable to regain control.
Vincent said Friday that the Federal Aviation Administration is investigating the crash.
Enid is about 85 miles north of Oklahoma City.