In the finals, Elistratov covered the distance for two minutes and 10.687 seconds.
Korean skater Kim Hyo-jun took gold and Dutch skater Sjinkie Knegt took silver.
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Elistratov thus brought the first medal for the team of "Olympic Athletes From Russia" at the Pyeongchang Olympics.
Russian Olympic Committee (ROC) chief Alexander Zhukov told Sputnik that "it was important to win a medal on the first day as it improves the mood of the whole team."
The official opening ceremony of the Olympic Games took place on Friday. The Games will end on the 25th of February with the closing ceremony.