On June 29, 2004, about 0830 mountain daylight time, a Sheppard Kitfox IV airplane, N316R, sustained substantial damage while landing at Rigby-Jefferson County Airport, Rigby, Idaho. The airplane was operated as a visual flight rules (VFR) local flight under the provisions of 14 CFR Part 91 when the accident occurred. The first pilot, an airline transport pilot seated in the right seat, and the second pilot, a private pilot seated in the left seat, were not injured. Visual meteorological conditions prevailed and no flight plan was filed for the flight. The flight originated at Rigby-Jefferson at 0800. During a post-accident telephone conversation with a representative from the National Transportation Safety Board (IIC), the first pilot reported that the second pilot was checking him out in type. He stated the second pilot completed the first landing on runway 19. Following the successful landing, the first pilot attempted a landing on the same runway. He stated that shortly after touchdown, during the landing roll, the airplane veered to the right. The first pilot applied brakes and corrective action, however, the airplane continued to track to the right. The airplane eventually exited the runway, encountered soft muddy terrain and nosed down. The airplane sustained substantial damage to the left wing and wing lift strut. Damage was also noted to the left landing gear wheel assembly (outer rim bead) and landing gear attach bracket. The left-hand tire separated from the wheel assembly. The left-hand forward gear bracket bolt (AN-5-20A) was found in its installed position. The first pilot reported that the associated washer and nut were later located on the runway, right of the runway centerline, between the point of touchdown and where the airplane came to rest. Thread shear and stripping was noted to the nut, and remnants of the threads were found on the bolt grip.