On the border with Georgia, miles-long queues of vehicles have formed including men trying to escape the war.
One man, who did not want to be named, told the BBC he had grabbed his passport and headed to the border, without packing anything else, immediately after President’ Putin’s announcement - because he fell into the group that could potentially be sent to the war.
Some witnesses estimated the queue of cars at the Upper Lars checkpoint to be some 5km (3 miles) long, while another group said it had taken seven hours to get across the border. Video from the scene showed some drivers leaving their cars or trucks temporarily in standstill traffic.
Georgia is one of the few neighbouring countries that Russians can enter without needing a apply for a visa. Finland, which shares a 1,300km (800 mile) border with Russia, does require a visa for travel, and also reported an increase in traffic overnight.
Airline tickets to Istanbul, Belgrade or Dubai , which have not banned Russian flights, saw ticket prices soar immediately after the military call-up was announced. Meanwhile flights to non-visa destinations can cost thousands of euros.
Germany’s interior minister indicated on Thursday that Russians fleeing the draft would be welcome in her country.
Nancy Faeser said deserters threatened by “severe repression” would receive protection on a case-by-case basis, following security checks. Meanwhile thousands of protesters have taken part in demonstrations across Russia against Putin’s announcement of a ‘partial mobilisation’.
Russia claims the reports of men fleeing are exaggerated.