Described are medical graft products, systems, and methods for treating fistulae.Certain products of the invention are configured to have portions residing inand around a primary fistula opening, e.g., one occurring in a wall of the alimentarycanal. One such product includes a biocompatible graft body which is configuredto block at least the primary opening. The graft body includes a capping member,which is configured to contact portions of the alimentary canal wall adjacentto the primary opening, and an elongate plug member extending from the cappingmember, which is configured to extend into at least a portion of the fistula. Incertain embodiments, a graft body component has the capacity to expand or otherwisechange form to provide a suitable capping arrangement. Such a component can includea resilient wire frame, e.g., one that is self-expandable or one that requiresat least some manipulation in order to expand.