Wood carvings, birchwood boxes, and lacquer boxes are typical souvenirs of Siberia. A few hotels have souvenir stalls in the lobby, and the Regional Museum at Ul. Karla Marksa 2 has a decent selection in their gift shop as well.
Kamusi are winter boots used by native Siberians made out of deer, elk, or other fur. One place to buy is at a small shop across from the bus station at Ul. Oktyabrskoi Revolyutsii 20B called "Aikhal". It is in a courtyard behind some kiosks, so it takes some searching. They have kamusi for men, women, and children, with prices starting at about 3000 Rubles.