Hacham Raphael Elashvili was born to Rivka and Joseph on 29 Nissan, 5694 (1934) in Kolashi, West Georgia. His mother was the daughter of Hacham Aharon Boterashvili, the spiritual leader of Kolashi, West Georgia. At the end of World War II, Hacham Raphael's parents moved to the city of Zugdidi to seek their livelihood. In 1948 Hacham Raphael Elashvili returned to Kolashi and lived in the home of his grandfather, Hacham Aharon Boterashvili who, along with Hacham Michel Ajiashvili, taught him Torah.
Hacham Raphael Elashvili married in 1953. In 1954 he moved with his wife to the city of Gori to serve as the Jewish community's cantor, returning to Kolashi in 1958 to serve as cantor of the city's Great Synagogue.
In 1972 Hacham Raphael Elashvili immigrated to the Land of Israel with his family and parents. He settled in the city of Lod, and served as Chief Rabbi of the Georgian Jewish community in Israel.
Hacham Raphael Elashvili passed away on 23 Sivan, 5765 (2005) and was buried in Lod.
Hacham Raphael Elashvili wrote a commentary on Ethics of Our Father, Pirkei Raphael, published with elaborations written by his student.