Bjarne Undheim (12 January 1905 – 28 May 1988) was a Norwegian educator and politician for the Centre Party.
He was born in Time. He obtained a cand.real. degree from the University of Oslo in 1930 and worked as a teacher and later principal at high schools in Rogaland.
He was elected to the Norwegian Parliament from Rogaland in 1961 and was re-elected once.
Undheim was mayor of Time during the term 1955–1959.