The wedge type rail clamp compresses the rails with small clamping force at first, and with large clamping force when the wind speed increases because of the wedge working. If the supporter is not installed in the rail clamp with V-type wedge when the wind speed increases more and more, the structure will occur overload which leads the structure to fracture. But in the clamp with U-type wedge the supporter is not necessary because the tangential angle of the wedge increases as the sliding distance increases. The proper shape of U-type wedge is determined by the initial clamping force and the tangential angle of the wedge. Accordingly we, first carry out the finite element analysis in order to analyze the relation between the sliding distance and the wedge angle. Next we suggest the proper shape of U-type wedge as analyze the relation between the radius of curvature and the sliding distance.