The crash happened around 10:30 a.m. at Capital City Airport, according to Franklin County dispatchers.
According to Naitore Djigbenou, spokeswoman for the Kentucky Transportation Cabinet, the twin-engine aircraft is based out of Lexington and was doing instructional training at the time of the crash.
Frankfort Fire Department Chief Wayne Briscoe said the aircraft caught fire, but both occupants were already out of the plane when the first fire crews arrived. Heavy fire was reported coming from the left side of the plane. The flames were quickly knocked down by fire crews.
Briscoe said both occupants declined medical treatment.
According to the FAA website, the plane is a Beech 76 twin engine aircraft built in 1979. It is registered to a leasing company in Wilmington, Delaware.
Djigbenou said the aircraft off off the runway and the airport remains open.
The FAA will conduct an investigation into the crash.