The ATR-72, a French-Italian-made twin-engine turboprop, operated by UTair was flying from Tyumen to the oil town of Surgut with 39 passengers and four crew.
The aircraft went down on a snowy field outside Tyumen, a major regional center in Siberia about 1,700 kilometers (1,000 miles) east of Moscow. The cause of the crash was not immediately clear.
UTair published a list of the passengers and crew, and none of them appeared to be foreigners.
The Emergency Situations Ministry first said 12 survivors were flown by helicopter to a Tyumen hospital, but that one of them had died. The ministry's regional branch in Tyumen later said that a 12th survivor was in a village hospital and revised the death toll downward to 31.
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 crash in Yaroslavl, a city 250 kilometers (150 miles) northeast of Moscow, in September 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.