The first element is the genitive case of the Old Norse male name Vifill and the last element is the plural form of staðr which means "homestead" or "farm", therefore it means "Vifill's homestead".

The official blazon is "Azure, three inverted couped chevrons argent, two and one" (Norwegian: I blått tre omvendte svevende sølv sparrer, 2-1).

This means the arms have a blue field (background) and the charge is three V-shaped figures (two over one).

The V-shapes have a tincture of argent which means it is commonly colored white, but if it is made out of metal, then silver is used.

The lake Søre Vistvatnet lies in the southeastern part of the municipality inside the national park.

The municipal council (Kommunestyre) of Vevelstad is made up of 13 representatives that are elected to four year terms.

The tables below show the current and historical composition of the council by political party.