This paper develops a stylized model of international treaty formation and analyzes the different modalities with which states can become part of an international treaty according to the procedures set forth by the Vienna Convention on the Law of Treaties. We consider the rules governing accession to international treaties, distinguishing between three situations: (i) Treaties for which acceptance of a new member requires unanimous approval of the signatory states with an amendment of the original treaty agreement (closed treaties); (ii) Treaties where acceptance of a new member is made possible through approval by a majority of the existing member states (semi-open treaties); and (iii) Treaties where the original member states have agreed to leave the treaty open for accession by other states (open treaties).