The ATR-72 turboprop operated by UTair took off at 7:40 a.m. from Tyumen, a regional centre in Siberia about 1,700 kilometres (1,000 miles) east of Moscow, heading for the oil town of Surgut, about 650 kilometres (400 miles) away.
The plane came down in a field about three kilometres (two miles) away from the Tyumen airport, breaking into three sections upon impact. Part of it was destroyed by a fire that burned at least six people to death, said Sergei Kiselyov, the police chief at the Roshchino airport in Tyumen.
The cause of the crash was not immediately clear, but investigators said evidence so far points to a technical failure of the French/Italian-made twin-engine aircraft. They noted that witnesses reported seeing smoke coming from its engines as the plane came down and said the pilots had tried to return to the airport.
The federal Investigative Committee said while equipment failure appeared to be the most likely cause of the crash, pilot error or mistakes by traffic controllers had not been ruled out.
All of the 39 passengers and four crew on board were Russian, according to a list by Utair.
"One survivor stood up on his own and waited until he was given medical help and only then felt worse," Kiselyov told the state news agency RIA Novosti.
Russia has seen a string of deadly crashes in recent years. Some have been blamed on the use of aging Soviet-era aircraft, but industry experts point to a number of other problems, including poor crew training, crumbling airports, lax government controls and widespread neglect of safety in the pursuit of profits.
Pilot error was blamed for a September crash in Yaroslavl, a Russian city 250 kilometres (150 miles) northeast of Moscow, that killed 44 people, including a professional hockey team.
Pilot error and fog also were ruled the main causes of a crash in April 2010 that killed Poland's president and 95 other people as their plane was trying to land near Smolensk, in western Russia.
The ATR-72 has been involved in several accidents in past years.
Most recently, one went down in bad weather in Cuba in November 2010, killing all 68 people on board. Cuban aviation officials said the investigation showed there was nothing wrong with the aircraft.
In August 2009, an ATR-72 flown by Bangkok Airways skidded off the runway and crashed into a building after landing in stormy weather on the Thai resort island of Samui, killing the pilot and injuring seven people.