Russian media reports that leading theory is multiple bird strike.
http://www.vremya.ru/print/185303.html (in russian)
According to unnamed experts who took part in the investigation the reason for engines 3 and 4 failure is "organic matter in the engine air intake". The pilots did their best in the situation but they had no chances. Technical side of the investigation is almost complete, it is now up to ornithologists to identify the species from the remaining few grey feathers.