Elizabeth M. Nielson (1905-1995) was a Mormon school teacher and genealogist in Utah.

Elizabeth Brazier Mitchell was born in Salt Lake City, Utah on April 28, 1905 to parents Joseph and Suzan Liberta Brazier Mitchell. She graduated from Granite High School and the University of Utah, then taught school in the Granite and Salt Lake School Districts and at the Kelsey Academy in Kelsey, Texas. She served as a missionary for the Church of Jesus Christ of Latter-day Saints in the Central States and Texas. She also served in several organizations within the Church, and was especially interested in genealogy. In 1958, she joined with the New Zealand Missionary Society Temple Dedication Tour, which also traveled to Hawaii and Fiji. On August 19, 1964, she married Ernest Eugene Nielson in Salt Lake City, Utah, and moved with him to Richfield and Manti, Utah until his death on May 14, 1973. At that time, she returned to Salt Lake City, and then to the suburb of Holliday, where she was active in several civic and service organizations. She died on October 27, 1995 in Holladay, Utah.