If you ask us to prove that plural marriage is biblical and acceptable to God, we're probably going to ask if you've read some of these items yet! "The truth is out there", and there are many written works available that provide sound biblical exegesis in support of biblical plural marriage, or just biblical marriage. We have picked what we think are some of the best available to get you started. Don't expect to agree with everything found in each book, but you should find something helpful in each resource.
We are pleased that at least six of the authors of books listed below have participated in Biblical Families forums or retreats. We look forward to making more great material available to you as we find it.
Tom Shipley's excellent book, Man and Women in Biblical Law, is a must have for anyone serious about digging into the biblical case for plural marriage. His second book in the series, They Shall Be of One Flesh, is available also (both books are available in text and pdf format). These books are meaty.
A great book for introducing people to the biblical argument for plural marriage is The Great Omission by Clyde L. Pilkington, Jr. Clyde runs Patriarch Publishing House, where you can pick up hard copies of many of these books, and others that may be of interest to you.
Why Do You Believe That? is a good choice for introducing family and friends to Biblical marriage, and thinking Biblically, not traditionally.
The now-famous 1869 book by "James Campbell" (pseudonym): The History and Philosophy of Marriage, or Polygamy and Monogamy Compared. Google ebooks now has the entire public domain book for free here. Choose Display Options//'Flowing Text' for a modern font. While you're on Google ebooks, do a search for 'polygamy'—there are some other interesting older books there that we've never seen elsewhere.
If you are seriously researching the history of Christian polygamy, After Polygamy Was Made a Sin by John Cairncross is a must-have. Here's a review by Sam Chapman. This out-of-print book is now available as a reprint here.
James Wesley Stiver's Eros Made Sacred, or The Biblical Case for Polygamy (free) presents a clear biblical justification for polygamous marriage.
The rediscovered classic Thelyphthora, or A Treaties on Female Ruin: In Its Causes, Effects, Consequences, Prevention, and Remedy; Considered on the Basis of the Divine Law, by Martin Madan, is available on Google Books: Volume 1 and Volume 2. It's not an easy read in this 1780 edition, but the content is very worthwhile.
Divorce and Re-Marriage: Recovering the Biblical View is available online in a Word version, or you can buy it at Amazon. The author, William F. Luck, is well known in evangelical circles. He's written a very biblically sound, scholarly, complete treatment on divorce and remarriage. In doing so, he found he couldn't ignore the implications regarding plural marriage, and was somewhat surprised by what he found. He was just being honest about the truth he found in the Word, making for a compelling argument. You may wish to start with Appendix B (On the Morality of Biblical Polygyny).