A surgical fastener of plastic or plastic-like material includes initially separate fastener and retainer members. The fastener member has at least two parallel prongs, each of which fits into a respective one of at least two apertures in the retainer member. The prongs twist as they enter the apertures. Then the prongs return to their initial orientation in which they interlock with the retainer member to form a finished fastener. The fastener is applied by forcing the fastener member prongs through the tissue to be fastened with the aid of metal pins contiguous with each prong. The pins are automatically withdrawn from the tissue after the prongs interlock with the retainer member and before the fastened tissue is removed from the fastener applying apparatus.