It would appear that polygamy is something that is tolerated rather than approved. Just as Jesus noted that Moses allowed divorce because the people’s hearts were hard, it seems as if polygamy is something that is less than ideal.
The first instance of polygamy in the Bible is early in Genesis 4:19. Lamech is noted to have two wives. Lamech is also very wicked and boasts about killing a man for wounding him. While we shouldn’t associate polygamy with wickedness just for this reason it is noteworthy that our first instance of polygamy comes from a very wicked man.
There is one place in the Bible that allows for polygamy. In a levirate marriage a man is called upon to marry his brother’s widow in the event of his brother’s death. This assured that the widow would be taken care of. It also allowed for the brother’s line to continue as all children born to the widow would be considered legally to be the brother’s and they would inherit the brother’s property.
Some suggest that polygamy occurs in the ancient world as a matter of convenience. This may or may not be the case, but here is the argument anyway. Because of wars and a more physical lifestyle, men died younger and often before reaching marrying age as they tended to be older than their brides. This created a shortage of available husbands. Because women were most often untrained and uneducated they required a man to protect them. While the father could take of them eventually he would die so it was far better to be a second wife to a man than to be left to fend for herself. Whether this was actually the thinking of the time is questionable but the argument does make sense.
There is a very good and spiritual reason why men are allowed multiple wives but women are not allowed multiple husbands. It is to preserve the sanctity of the family. If a man with multiple wives impregnates his wife, it is clear who the father and mother are. However, if a woman has multiple husbands and she becomes pregnant, it is not clear who the father may be.
While there is not a recorded command forbidding polygamy by the time of the New Testament it did not exist. Polygamy was not an issue in the Roman empire. 1 Timothy 3:2 states that church leaders should be “the husband of one wife.” This would seem to imply that spiritual leaders should not practice polygamy.