Elias Snitzer graduated from Tufts University in 1945 with a B.S. in Electrical Engineering and received his M.A. (1950) and Ph.D. (1953) in Physics from the University of Chicago. From 1954 to 1956, Snitzer worked at Honeywell Industrial Instruments Division on thermal detector technology.

He began teaching at the Lowell (Massachusetts) Technological Institute in 1956, but his career stalled in 1958 when he was called to testify before the House Un-American Activities Committee (HUAC), an investigative committee of the United States House of Representatives.

Snitzer was hired by American Optical (AO) where he began his work in optical fibers and lasers. In 1961, he demonstrated the first optical fiber laser and the first fiber amplifier. Snitzer remained at AO as director of corporate research until 1977. He then moved to United Technologies Research Center (UTRC). From 1984 to 1988 he worked at Polaroid Corporation, where he directed research and development of fiber and integrated optics programs for communication, sensors, and photographic instrumentation. At Polaroid, Snitzer and his team first demonstrated the double clad fiber laser in 1988. In 1989, he joined the Ceramic Science and Engineering faculty of Rutgers University, where he continued to teach and research fiber laser amplifiers, glass, and fiber Bragg Gratings until his retirement in 2001.

An OSA member since 1961, Snitzer was named a Fellow in 1964. He received numerous awards and honors, including the OSA Charles Hard Townes Award (1991) and John Tyndall Award (1994); the IEEE Photonics Society Quantum Electronics Award (1979); the Otto Schott Research Award (1999); and the Rank Prize for the invention of the cladding pumped fiber lasers (2000). He was named a Life Fellow of the IEEE, and he was elected to the National Academy of Engineering in 1979 for the invention of the glass laser and the fiber-optics laser. The American Ceramic Society honored him with the Morey Award for glass science (1971) and as the inaugural recipient of the Stookey Award.