For the improvement of a train speed in the conventional line from overhead system point of view, it is necessary to approach not only in the aspect of the increasement of tension for catenary but the application of a pre-sag. A certain tension acting on a dropper is removed when it is slack by the pantograph passing. Right after the pantograph passes, the dynamic force caused by the mass of contact wire acts on the dropper. If the pre-sag is applied to the catenary, the static force on the dropper is increased. For the assurance of the safety for the dropper, it is necessary to predict the dynamic force. The purpose of this study is to predict and analyze the force on the dropper according to the applied pre-sag.