As Fulkerson Park Baptist Church is soon to vote on a new Constitution which (if passed) will transition our church governance structure from a Pastor-Deacon-led model to an Eldership model, I have spent a fair bit of time reading material on elders. Here is a select list of books on or related to eldership, with some brief comments.
Biblical Eldership: An Urgent Call to Restore Biblical Church Leadership by Alexander Strauch is the most thorough exegetical defense of biblical eldership that I have read. Strauch thoroughly covers every reference to elders in the New Testament, building a case for eldership which is marked by five characteristics: (1) It is Pastoral Leadership, (2) It is Shared Leadership, (3) It is Male Leadership, (4) It is Qualified Leadership, and (5) It is Servant Leadership. Strauch writes from a Brethren background and does not see a place for any kind of congregationalism. Another slight demerit of the book is its lack of discussion on practical issues such as transitioning to elders. But for getting into the text, this book is unsurpassed.
Biblical Eldership: Restoring the Eldership to its Rightful Place in the Church is a heavily abridged version of the longer book which presents the conclusions minus much of the detailed exegesis. It is a very useful tool for introducing the concept of eldership to lay-people.
Elders and Leaders by Gene Getz is a more popularly written treatment of elders that is especially helpful in discussing some of the more pragmatic concerns with eldership, such as the relationship between elders and pastoral staff. I found this book a helpful balance to Strauch's.
Mark Dever's The Deliberate Church: Building Your Ministry on the Gospel, discusses elders and a lot more besides. Sections 3 and 4 of the book on "Gathering the Elders" and "When the Elders Gather" are invaluable in giving practical and measurable steps for introducing the concept of elders to a church and patiently leading a church through the transition to eldership. Dever also embraces a view of eldership that does not totally displace congregationalism and is true to historic Baptist church polity. Chapter nine in Dever's Nine Marks of a Healthy Church also discusses biblical church leadership, and his A Display of God's Glory: Basics ofChurch Structure: Elders, Deacons, Congregationalism & Church Membership explores the issues further (this book can be read online in a PDF file). You might also want to check out other online resources (including some audio sermons and lectures) on elders at 9 Marks.
Mark Dever lent his endorsement (by writing the foreword) to a new book by Phil Newton called Elders in Congregational Life. You can read my review of this excellent book below.
The teaching of John Piper on Biblical Eldership has been especially helpful to me. His seminar on the topic can be downloaded and listened to at Biblical Training.org. Don't forget the booklet which goes with this seminar. You might also want to browse Piper's other stuff on Pastor and Elders, and his powerful book, Brothers, We Are Not Professionals.
Many good seminars relating to eldership and pastoral ministry (and other topics) are available for purchase (MP3 downloads) at the website for the Shepherd's Conference, hosted by Grace Community Church.
Some other books include John MacArthur's The Master's Plan for the Church, which is another helpful book on the church with several good chapters on elders; Joseph Stowell's Shepherding the Church, which doesn't really address eldership per se, but does have some fantastic material on the task of shepherding and pastoring in general. And Richard Baxter's classic The Reformed Pastor could hardly be surpassed in terms of outlining the essential responsibilities of elders (although I don't know of hardly any elders or pastors who live up to it!).
To come back around full circle, Alexander Strauch has also written Training Manuals for elders (which I have not read yet) and a life-saving little book (for me at least) on how to lead elders' meetings, called Meetings that Work: A Guide to Effective Elders' Meetings.
Finally, I am planning to post some of my own material on eldership, which briefly surveys the teaching of the New Testament, within another couple of days.