A queue of cars has been seen at the Russia-Georgia border.
Traffic at the crossing with Finland also increased after Russian President Vladimir Putin said he intended to mobilize 300,000 reservists to fight in Ukraine
Airline ticket prices out of Moscow have risen above $5,000 for one-way trips to the nearest foreign countries.
Most airline tickets are completely sold out for the next few days.
Sergei, a Russian man who declined to give his last name, told Reuters as he arrived in the Serbian capital, Belgrade: “It’s okay to be afraid of war, death and things like that.”