The 1783 Institution of the Society stipulates the conditions for membership.  “All the officers of the American Army, as well as those who have resigned with honor after three years’ service in the capacity of officers, or who have been deranged by the resolutions of Congress upon several reforms of the army, as those who shall have continued to the end of the war, have the right to become parties to this Institution.…”  A provision was also made for descendants of Continental officers who died during the war to become members.  

Male descendants of officers of Virginia state troops or Virginia Navy (not militia) may apply for hereditary membership in the Virginia Society.  (Each state society approves candidates for membership in the respective society, thereby admitting members to the General Society.)  Only one descendant and his successors (age 21 or older) may represent an eligible officer at any time.
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The basic qualifications of membership are defined in the Institution of the Society of the Cincinnati, adopted in 1783. The Institution provided for the admission of commissioned officers in the Continental and French service who had served to the end of the war and those who had resigned with honor after a minimum of three years' service as a commissioned officer. The Institution also provided for the admission of commissioned officers who had been separated from the army in a reorganization involving the merging of two or more units. 

The authors of the Institution provided for the admission of the "eldest male posterity" of each original member after the member's death. If an officer had no son, the Institution provided for the admission of "the collateral branches, who may be judged worthy of becoming its supporters and members." The Institution also allowed for the admission of "the eldest male branches" of officers who had died in service on the same basis as the children of members.

Until 1854, hereditary membership was restricted to hereditary representatives of original members and officers who died in battle. The descendants and collateral relatives of otherwise eligible officers who did not join the Society at its founding were deemed ineligible. In that year, the Society addressed its declining membership by adopting what has become known as the "Rule of 1854," which allows for the admission of hereditary representatives of officers who did not join the Society at its founding.

The Institution provided that each constituent society should "judge of the qualifications of the members who may be proposed" in a manner "consistent with the general maxims of the Cincinnati." In keeping with this provision, each of the fourteen constituent societies regulates admission according to local and historical circumstances.