According to Genesis, Shem was the ancestor of Asshur.
Genesis 10:22 lists Asshur among the sons of Shem, alongside Elam, Arpachshad, Lud, and Aram. In the genealogical framework known as the Table of Nations, Shem’s descendants are associated with peoples and regions of the ancient Near East. The name Asshur is also connected with Assyria, though the biblical genealogy and later historical identifications should not be treated as a complete modern population history.
Shem is one of Noah’s three sons, with Ham and Japheth. Genesis later traces a line from Shem through Arpachshad to Abram, making Shem especially important in the genealogy leading toward the patriarchal narratives.
The spelling varies across translations and languages: “Asshur,” “Ashur,” and “Assur” can refer to related forms of the name. The question uses the English form found in many Bible translations. The key relationship remains the same in Genesis 10: Asshur is listed as a son of Shem.