We cannot deny that a form of surrogate pregnancy occurs in Scripture. Abraham went into Hagar and impregnated her in order to have a son. Abraham (then called Abram) did this because his wife Sarah had not produced a son, Therefore, "Abram's wife Sarai took Hagar the Egyptian, her maid, and gave her to her husband Abram as his wife," (Gen. 16:3). In the culture of the time, the son born to Hagar would belong to Abram. There are other such examples where a slave was given to a man in order to bear children to his name. But, these slaves were given in marriage and considered secondary wives. This prevented the act of adultery though it permitted polygamy. So, we can conclude that such surrogate motherhood did not occur outside the bounds of marriage.
Conditions of unacceptability
It would not be acceptable for a woman to carry another couple's child if that women were to have sexual relations with the man who is not her husband in order to become impregnated. This would be adultery. Nor would it be acceptable for a man whose wife could not conceive to have sexual relations with a surrogate mother, who is not his wife. This would be adultery.
If the sperm of a man is deposited in the womb of a woman--without sexual intercourse--who is not his wife in order to obtain a child, this is adulterous since his seed is impregnating a woman who is not his wife.
What about a fertilized egg implanted in the womb of another woman? This would appear to be acceptable since the seed of the man does not enter the other woman. Instead, a fertilized egg is implanted, and the total genetic material is from the married couple.
Surrogate motherhood is permissible if there is no sexual intercourse and if the seed of the man does not enter the womb of a woman to whom he is not married via an already fertilized egg.
Finally, this fertilization method is not acceptable if it involves the killing of other fertilized eggs as is often the case with "test tube" fertilization.