Elmwood Township was named for the groves of elm trees along the Buffalo River.

[3] According to the United States Census Bureau, the township has a total area of 35.7 square miles (92 km2), all land.

As of the census[1] of 2000, there were 371 people, 135 households, and 115 families residing in the township.

There were 147 housing units at an average density of 4.1 per square mile (1.6/km2).

12.6% of all households were made up of individuals, and 3.7% had someone living alone who was 65 years of age or older.