According to a statement posted on the museum's Instagram account, Yanks Chief Operating Officer Frank Wright and Pilot-in-Command Michael "Mike" Gilles were killed in the crash.
The Federal Aviation Administration said the twin-engine Lockheed 12A Electra Junior crashed shortly after 12:30 p.m. Saturday, just west of Chino Airport. The crash occurred during the Yanks Air Pops & Props event, although it was not immediately clear whether that plane was part of the show.
Firefighters doused the flames within 10 minutes before finding Wright and Gilles dead inside.
Gilles of Aliso Viejo had been the Pilot-in-Command of the Lockheed 12A for Yanks for the last several years.
"Mike flew as captain on the Lockheed 12 in the left seat on the day of the incident," read the statement from the museum. "The airplane was not required to have two rated pilots on board, but Frank assisted in flying procedures and operations from the right seat."
Friends of Wright who spoke with Eyewitness News identified him over the weekend.
One witness who was at the Father's Day event said Wright and Gilles had just participated in a panel discussion at the museum moments before the crash.
Meanwhile, the museum remains closed until further notice.
"Yanks is still cooperating with authorities in their investigation of the incident," continued the statement. "Several people close to Yanks have been invaluable in their assistance to the families during this tragedy, and we would like to thank them as well as everyone who has expressed their condolences and support over the last few days."
It's unclear what caused the plane to crash. The FAA said that agency and the National Transportation Safety Board will investigate the crash.
ABC News contributed to this report.