The purpose of this study is to derive the damage weak part of the elastic rail fastening system for concrete tracks (System 300-1). In the concrete tracks, the elastic rail fastening system sticks the rail and the sleeper and reacts all the time when the train is running. Among the components of the rail fastening system, the resilience pad and tension clamp were fatigue members and were constantly deformed in response to compressive and uplift forces. In this study, the residual deformation characteristics of the tension clamp according to the period of use were analyzed using by specimens taken on site in the same section for 6, 11, and 16 years on the serviced urban transit. In addition, the damage mechanisms for each component were derived based on finite element analysis. As a result of the numerical analysis, the stress (strain) of each part of the tension clamp according to the external force from the applied clamping force was analyzed to derive the damaged weak part of the tension clamp.