It was instituted in 1934 "to encourage the study and to advance the knowledge of the history of Scots Law,"[1] and is named after James Dalrymple, 1st Viscount of Stair, the seventeenth century Lord President of the Court of Session considered the most important of Scots Law's Institutional Writers.

It can compared to the Selden Society, an organisation devoted to the study of English legal history.

The Society's Literary Director is Mark Godfrey, Professor of Legal History at the University of Glasgow School of Law.

The Society previously provided a postgraduate scholarship to support someone undertaking doctoral research in Scots legal history.

The scholarship has had one successful graduate, Dr Thomas Green, who is now a lecturer at the University of Aberdeen School of Law.