The aircraft crashed shortly before 11 am on Saturday, the Ohio State Highway Patrol said. It had taken off from Springfield Beckley Municipal Airport.
Police identified the dead men as Don Gum, 73, and Mitchell Cary, 65, both from Ohio.
The plane in Saturday's fatal crash, known as "Silver Bird," was a flyable look-alike of Wilbur and Orville Wright's first production aircraft, the Wright Model B Flyer.
It was designed and built by volunteers from Wright "B" Flyer Inc., a nonprofit organisation based at Dayton-Wright Brothers Airport in Miami.
Both pilots had extensive experience flying the biplane, built by a company that uses the planes to promote public awareness of Dayton as the birthplace of aviation.
There have been at least four other crashes in the last decade of replicas or reproduction Wright brothers planes, including one in the Dayton area that left a man seriously injured,
Dayton Daily News reported.
The cause of the crash remained under investigation, according to the highway patrol. It's looking into the incident along with the Federal Aviation Administration and the National
Transportation Safety Board.
The plane began test flights in June and performed well, according to a press release on the organisation's website.
Gum and Cary were members of the group's board of trustees and Cary was a former president.