Robert Washington Fyan (March 11, 1835 – July 28, 1896) was a U.S. Representative and soldier from Missouri.

Born in Bedford Springs, Pennsylvania, Fyan attended the common schools.

He studied law and was admitted to the bar in 1858; commencing practice in Marshfield, Missouri.

In June 1861 he entered the Union Army to fight in the American Civil War.

Robert Fyan sentenced Joseph Core as follows: 'he was to be taken to the place of execution and there be hanged by the neck until he be dead.'