A prosthetic tricuspid remodeling annuloplasty ring having two free ends can be configured to be stiff in the XY plane and relatively flexible along the Z axis. A tricuspid ring can be provided with a substantially elliptical shape in the XY plane, and a saddle shape in the Z direction. Disclosed tricuspid rings can include an inner core, an elastomeric interface, and an outer fabric covering. In some embodiments, the inner core can include a plurality of stacked layers of different materials. In some embodiments, the inner core can be formed of a single material and sized specifically to create a tricuspid ring that has a greater stiffness in the XY plane than along the Z axis.
