A member of the Oberlin faculty for ten years, Joseph Eliash was an renowned expert on Shi'i Islam. He was born in Jerusalem on October 25, 1932. His father Ysrael Eliash was a surgeon and his mother Naomi Eliash was a homemaker. Joseph Eliash studied at the Hebrew University in Jerusalem where he earned the B.A. in 1958 and the M.A. in 1962. He then undertook doctoral studies at the University of London, earning a Ph.D. in Islamic studies in 1966.

Eliash came to the United States in 1967 on a post-doctoral fellowship at the Center of Near Eastern Studies, University of California at Los Angeles, with support from the Ford Foundation. He taught at UCLA from 1967 until 1971 when he was named assistant professor of Jewish studies at Oberlin College.

Oberlin's Judaic and Near Eastern Studies Program was established in 1972, and Eliash served as the Program Director from 1972 to 1981. His courses included Arabic, Hebrew, Islamic studies, and history of Judaism. He was promoted to associate professor in 1974.

In 1972, he received an H. H. Powers Travel grant and grant-in-aid from Oberlin to edit and translate the sixteenth century Persian manuscript "Chronicles of Baba-y-Lutf." He was invited to read to papers at numerous conferences, including the 1973 International Conference of Orientalists at the Sorbonne in Paris, the 1976 International Conference of Jewish Studies in Jerusalem, and the 1979 Conference on Islam and the Modern World at al-Azhar University, Cairo.

From 1978 until his death in 1981, Eliash pursued research under a grant from the National Endowment for the Humanities, supplemented by a Smithsonian Institution grant. With these grants, he undertook to edit and translate selections from the Shi'i Muslim corpus of oral tradition. In 1980 Eliash received media attention when he publicized some of the conclusions that he had drawn from this research, namely that Ayatollah Ruhollah Khomeini had violated Shi'i Muslim law by holding fifty-two American citizens hostage.

Joseph Eliash was one of five Oberlin residents to become a naturalized U.S. citizen in November 1976.

He married Lily Wolf on March 18, 1954. They had two children, Adi (born January 25, 1958) and Anat (born May 26, 1959), and the couple later divorced. In 1974, Eliash married Dorothea Gallup, assistant professor in the Judaic and Near Eastern Studies Program. She died of cancer on May 16, 1977, in Munich, Germany.

Joseph Eliash died of a heart attack on March 30, 1981, in Oberlin, Ohio.