The river's source is on the northern slopes of the Greater Caucasus in Khevsureti from where it flows north and crosses into Russia. The Assa accepts the Gulaykhi from the right and flows through the Erzi Nature Reserve. North of the stanitsa of Nesterovskaya, the Assa turns east, crosses into Chechnya, flows through the stanitsa of Assinovskaya, and accepts the Fortanga from the right. The mouth of the Assa is at the locality of Zakan-Yurt. The principal tributary of the Assa is the Fortanga (right).