On August 10, 2013 about 1400 eastern daylight time, a Perth Amboy, model BIRD BK, airplane, NC727Y, impacted terrain during a runway excursion after landing at the Parr Airport (42I), Zanesville, Ohio. The pilot was not injured. The airplane was substantially damaged. The airplane was registered to a private individual and operated by the pilot under the provisions of 14 Code of Federal Regulations Part 91 as a personal flight. Visual meteorological conditions prevailed for the flight, which was not operated on a flight plan. The flight originated from the Greater Cumberland Regional Airport, Cumberland, Maryland, about 1130.The pilot reported that after landing he noticed that the runway was rough, so he decided to exit the runway and taxi on the grass to preserve the tires on the antique airplane. Soon after leaving the runway, he encountered an unmarked drainage ditch, which the airplane went into. The airplane was an antique biplane and sustained damage to the fuselage, right main landing gear and both right wing spars. Runway 10 at 42I was a paved asphalt surface, 3,100 feet long and 26 feet wide. About 30 feet to either side of the runway's paved edge were rows of runway lights spaced about 100 feet apart. On the south side of the runway, the grass was mowed to a short height for about 40 feet from the south edge of the paved runway. South of this mowed area was an area of taller vegetation that was about 1 foot in height. Visible in the grass areas were tire tracks from the accident airplane which showed that it exited the south side of the runway about 150 feet from the approach end. The tracks proceeded through the short mowed grass area to where a broken runway light was at, and then continued into the taller vegetation. The tire tracks continued to a drainage ditch that was in the taller vegetation. The drainage ditch was about 500 feet from the approach end of the runway. Impact scars were visible near the ditch. Although the runway exhibited patched cracks in the pavement, it did not have a rough appearance.