Aspects of the invention are directed to a ceramic matrix composite ring seal segment. The ring seal segment according to aspects of the invention includes a relatively simple body that is circumferentially curved. At least a portion of the hot gas path surface of the ring seal segment can be coated with a thermal insulating. material. In one embodiment, each ring seal segment can be operatively connected to a stationary support structure, such as by way of isolation rings. The ring seal segments and/or the isolation rings can be configured so as to restrain the ring seal segments in the axial, radial and/or circumferential directions. The ring seal segments can be attached to the isolation rings so that the support points act opposite the operating pressure loads. Thus, the ring seal segments carry these loads in compression, a strong direction of the CMC fibers.