The six-year-old cat - who has criminal gang tattoos on his face, back and chest - jumped out of the car window during a visit to the village of Pervomaisky, near Yekaterinburg, and ran off into the night.
It is feared that Bes may have ventured into a nearby forest, which is home to brown bears, wolves, wolverines, sable and lynx.
Mr Shafiev, 35, said he has been looking for Bes for five days to no avail and had been 'taking sedatives by the handful' since he vanished.
He said: "He jumped out of the window, disappeared into the darkness and tall grass.
"I searched for it myself everywhere, I called for the cat, it was useless.
"I'm very worried. I'm not eating, not sleeping."
Mr Shafiev has been widely criticised in the past for tattooing Bes.
Elizaveta Skorynina, an animal rights campaigner, said: "A person can choose to endure the pain in order to wear this 'beauty' later on in life, but the animal is not given the right to choose.
"This is purely desire of the owner. It is impossible to guess what pain threshold a cat finds impossible.
"Under general anaesthetic an animal can suffer side effects. Using 'muscle relaxants', the pet does not move but at the same time it feels and understands everything.
"I see nothing positive in such an experience."
Daria Polyanskaya, who runs a cat rescue charity, agreed, arguing that it was unethical because the cat can't consent, claiming that 'for a cat, this procedure is painful, comparable to a burn'.
Featured Image Credit: East2West News