Francis "Frank" Armstrong (3 October 1839 – 15 June 1899) was the fifth mayor of Salt Lake City, serving from 1886 to 1890.

He became friends with David Whitmer, one of the Three Witnesses for the Book of Mormon.

He married his first wife Isabella Siddoway on 10 December 1864, and they resided in Salt Lake City permanently.

He also polygamously married Sarah Carruth in 1870 and Maren Jensen in 1887.

Armstrong was elected as Mayor of Salt Lake City in 1886.