The YAK 52 aircraft crashed at 14:55 GMT in a field near Cooksmill Green on the A414 west of Chelmsford in Essex.
Firefighters called to the scene reported that "the plane was completely alight" when they arrived.
The plane had taken off from the nearby North Weald airfield. Both victims' next of kin have been informed, police said.
Rebecca Larsen told BBC News: "I witnessed the plane go up in flames. Cars pulled up on the left lane and everyone ran towards the burning plane."
Police closed a section of the A414 between Chelmsford and Ongar while emergency services attended.
Alison Hodgkins-Brown, at the scene for BBC Essex, said: "I can see the plane has come down in the middle of an oil seed rape field next to the A414.
"It's completely covered by tarpaulin and there are about eight police officers in attendance."
Sam Gildersleeve, from Ongar, was having lunch with friends when he saw the plane flying low.
"At this point we all looked at the sky and the plane attempted to do a somersault unsuccessfully, we heard a popping sound and noticed the plane did not re-emerge," he said.
"We then noticed smoke coming from the site in the field where the plane had crashed. Shortly after the emergency services appeared."
The Air Accident Investigation Branch has sent a team to investigate the crash.
Two men have died when a light aircraft crashed into a field and burst into flames, police have said.