Abstract: Based on an investigation of the mechanical characteristics of cables under different working conditions, cables can be categorized into two types, those with a given unstressed length and those with a given tension force. Two new cable elements are developed by using first-order expansions of the analytical solutions for the catenary cable and introducing appropriate constraint conditions, and explicit expressions of element tangent stiffness matrices are derived. A new iteration algorithm is then proposed for solving nonlinear structural responses, in which the influence of elastic deformations on the cable is included through an equivalent self weight per unit length. The erection process of a cable-stayed cantilever structure is considered as an example. The proposed method and an existing method are applied to the structural analysis of the structure under different loading conditions. The numerical results are presented and compared to show the efficiency and accuracy of the proposed elements and algorithms.