is a municipality in Innlandet county, Norway. It is located in the traditional district of Østerdalen. The administrative centre of the municipality is the town of Elverum. Other settlements in the municipality include Heradsbygd, Sørskogbygda, and Neverlia. Elverum lies at an important crossroads, with the town of Hamar to the west, the town of Kongsvinger to the south, and village of Innbygda and the Swedish border to the northeast. It is bordered on the north by Åmot municipality, in the northeast by Trysil municipality, in the southeast by Våler municipality, and in the west by Løten municipality.
The municipality is the 87th largest by area out of the 356 municipalities in Norway. Elverum is the 58th most populous municipality in Norway with a population of 21,435. The municipality's population density is and its population has increased by 6.4% over the previous 10-year period.
The parish of Elverum was established as a municipality on 1 January 1838 (see formannskapsdistrikt law). The borders have not changed since that time.
The municipality (originally the parish) is named after the old Elverum farm (Alfarheimr) since the first Elverum Church was built there. The first element is the genitive case of elfr which means "river" (referring to the Glomma river). The last element is heimr which means "home" or "farm".
The coat of arms was granted on 9 December 1988. The official blazon is "Gules, an owl displayed Or" (I rødt ei gull ugle med utslåtte vinger). This means the arms have a red field (background) and the charge is an owl. The owl has a tincture of Or which means it is commonly colored yellow, but if it is made out of metal, then gold is used. This design is a symbol for wisdom and teaching, since Elverum has a number of schools in it. Most owls are forest birds, and the owl can also represent wild animals and birds, and thus symbolize the forest and wilderness areas in and around Elverum. Finally, the owl has lifted wings and claws out which symbolize a determined defense and the fighting spirit of Norwegians.