Both main landing gears on a tailwheel-equipped homebuilt airplane collapsed during the landing roll. The 34,000-hour airline transport pilot, who was not the owner, reported that during the landing roll on the 6,000-foot-long, by 150-foot-wide asphalt runway, he began to apply "slight braking pressure." The pilot reported that the single-engine airplane began to "shudder rapidly." The left main landing gear collapsed, and immediately following that, the right main landing gear also collapsed. The radial engine powered airplane came to rest on the centerline of runway 14 and the pilot exited the airplane unassisted without injuries. Examination of the airplane by an FAA inspector, revealed that the left wing sustained structural damage; however, he was unable to determine the reason for the failure of the landing gear. The winds at the time of the mishap were reported from 140 degrees at 8 knots. **This narrative was modified on September 28, 2007.**