Voters are being asked to decide a successor to Roger Emmett as councillor for Hambleden Valley on Wycombe District Council. Councillor Emmett, a Conservative, died of a heart attack in July.
The election is being contested by three candidates.
Roger Metcalfe, of Fawley Green, is standing for the Conservatives. Mr Metcalfe spent 28 years as a Royal Artillery officer and now runs a business consultancy in Henley. Julian Grigg, from High Wycombe, is standing for the Labour Party and Brian Mapletoft is the UKIP candidate.