This study presents a elastic parabolic cable element for initial shaping analysis of cable structures. First, the compatibility condition and the tangent stiffness matrices of the elastic catenary cable element are shortly summarized. Next the force-deformation relations and the tangent stiffness matrices of the elastic parabolic cable elements are derived from the assumption that sag configuration under self-weights is small. To confirm the accuracy of this element, initial shaping analysis of cable-stayed bridges under dead loads is executed. Finally, the accuracy and the validity of the analysis-results are compared and analyzed through numerical examples.