A module flexible ligament damper includes an cylindrical inner structure with a central axis and an outer cylindrical surface. An outer casing with an inner cylindrical surface is positioned around the inner structure. A modular ligament with an inner flange and an outer flange connected by a web is positioned between the inner structure and the casing. The inner flange is connected to the inner structure and the outer flange is connected to the casing to support the inner structure within the casing, and to permit free orbital movement of the inner structure on a plane perpendicular to the axis of the inner structure. In one embodiment, the web is straight but does not intersect the axis of the inner structure for flexing in a radial direction. In other embodiments, the web is curved for radial flexing.