Robert Washington Fyan (March 11, 1835 - July 28, 1896) was a U.S. Representative from Missouri.
Born in Bedford Springs, Pennsylvania, Fyan attended the common schools. He studied law. He was admitted to the bar in 1858 and commenced practice in Marshfield, Missouri. County attorney in 1859. He entered the Union Army in June 1861, serving with Colonel Hampton's regiment, Webster County Home Guards, the Twenty-fourth Regiment, Missouri Volunteer Infantry, and the Forty-sixth Regiment, Missouri Volunteer Infantry. Circuit attorney in 1865 and 1866. Circuit judge of the fourteenth judicial circuit of Missouri from April 1866 to January 1883. He served as member of the State constitutional convention in 1875.
Fyan was elected as a Democrat to the Forty-eighth Congress (March 4, 1883-March 3, 1885).
Fyan was elected to the Fifty-second and Fifty-third Congresses (March 4, 1891-March 3, 1895). He resumed the practice of law. He died in Marshfield, Missouri, July 28, 1896. He was interred in Lebanon Cemetery, Lebanon, Missouri.