On August 29, 1996, about 1553 eastern daylight time, a Boeing 737-300, N392US, registered to Security National Bank Trust, and operated by USAir Inc., as flight 232, a 14 CFR Part 121 scheduled domestic passenger flight from Tampa, Florida, to Indianapolis, Indiana, encountered severe turbulence, about 45 miles south of the Chattanooga VOR, while in cruise flight at FL350. Visual meteorological conditions prevailed and an IFR flight plan was filed. The airline transport rated captain, first officer, 3 flight attendants, and 79 passengers were not injured. Three passengers sustained serious injuries and one passenger sustained minor injuries. The airplane sustained minor damage. The flight originated from Tampa, Florida, at about 1435. The captain diverted to Chattanooga, Tennessee, and landed without further incident. The captain stated he was in cruise flight at FL350 in visual flight conditions about 45 miles south of Chattanooga. The weather radar was on the 80-mile range with no weather present. The airplane encountered severe turbulence. A flight attendant notified him that they had sustained injuries in the cabin area. He contacted ATC after assessing the situation, and requested to divert to Chattanooga, which was approved. The digital flight data recorder was removed from flight 232, and shipped to the NTSB laboratory in Washington, D.C. for retrieval and analysis. Examination revealed that flight 232, was at an altitude of about 35,000 feet msl when the airplane was subjected to severe vertical acceleration oscillations. The vertical acceleration peaked at 1.81 g's, -1.38 g's, 1.99 g's, and continued to oscillate for 28 seconds. (For additional information see NTSB Solid State Flight DATA Recorder Factual Report.) Review of geostationary operational environmental satellite (GOES) 8 data shows an area of active convection from about 15 to 40 nautical miles east of (GQO) Choo Choo VOR. The GOES 8 visible images does not show any significant convection in the area 45 miles south of GQO. (For additional information see NTSB Meteorologist's Factual Report.)