The victims are believed to be a flying instructor and his pupil.
Emergency services were alerted that the plane was missing at around 4pm. About two hours later the burning wreckage of the plane was spotted by the crew of a rescue helicopter. The plane had crashed around one kilometre north of the airfield in Tidaholm.
The instructor had planned to use the plane at around lunchtime to practice take-off and landing with pupils. The accident is believed to have taken place during one of these exercises, but this has not yet been confirmed.
The fire was extinguished on Tuesday evening, according to police from nearby Skövde.