Regional governor,Igor Kobzev revealed that the fighter aircraft landed on a two-storey house in the city of Irkutsk.
The governor said he was at the scene and both pilots had been killed, but no residents were hurt.
According to the Russian Ministry of Emergency Situations, the jet was on a test flight when it came down.
Footage on social media showed the plane diving almost vertically before crashing in a fireball, sending thick black smoke into the sky.
Another video depicted firefighters putting out the blaze.
Russia’s state Investigative Committee said it had opened a criminal investigation into violations of air safety rules.
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