Allen Lowell Shields (May 7, 1927 – September 16, 1989) was an American mathematician who worked on measure theory, complex analysis, functional analysis and operator theory, and was "one of the world's leading authorities on spaces of analytic functions." Shields was a student of Witold Hurewicz. A special issue of The Mathematical Intelligencer, for which he served as editor of the "Years Ago" column, was dedicated to his memory in 1990.