SANHS is governed by an elected Board of up to 16 trustees who delegate the day-to-day management of the Society to the Executive committee.

The Society has six interest committees, involved with Archaeology, Historic Buildings, Local History, Natural History, Library & Archives, and Publications. Among other things, these committees organise events, carry out and publish research, and award SANHS grants.

There is also a Heritage Grants Committee, responsible for administering the Maltwood & Gray funds, and a Museum Collection Panel, responsible for the SANHS collections, in partnership with the South West Heritage Trust.

Applications from members to join any of these committees, whether governance or interest, is encouraged; the more people involved in the Society, the more able it is to carry out its charitable objects.