A ring structure with a metal design for a moving blade of axially flowed through compressor and turbine stages, particularly in gas turbine engines is provided. The ring structure includes a circular ring-shaped outer wall, a circular ring-shaped inner wall, which is located at a short radial distance from the moving blade tips, and includes a joining structure provided in the form of hollow chamber structure between the outer wall and the inner wall. The outer wall is provided in the form of a closed, mechanically stable housing wall of the compressor or turbine stage, and the joining structure provided in the form of hollow chamber structure is joined in a fixed manner to the outer wall and to the inner wall, for example, by soldering, diffusion welding or other joining techniques. The inner wall is provided in the form of a closed, mechanically stable structure, which serves as a run-in lining for the moving blade tips and which is made of a metal woven fabric and/or of a metal felt.