Elya Svei was born in Kaunas, Lithuania, where his father Shmuel Leib Svei was a rabbi. When he was nine years old, he moved to the United States to join his father, who was fundraising there.[2] In the United States he attended Yeshiva Torah Vodaath, graduating its Hebrew Parochial High School division in 1941.[3]
Svei was a student of Aharon Kotler.[4] He was a member of the Moetzes Gedolei HaTorah and chairman of the Rabbinic Administrative Board of Torah Umesorah until he resigned from both in June 2002, reportedly due to an ideological dispute with his colleagues.[5]
Svei was a founder of Sinai Academy in Brooklyn,[6] a middle school and high school catering to the children of primarily non-observant Russian Jewish immigrants.