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In this paper, the nonlinear mechanical response of elastic cable structures under mechanical load is studied based on the discrete catenary theory. A cable net is discretized into multiple nodes and edges in our numerical approach, which is followed by an analytical formulation of the elastic energy and the associated Hessian matrix to realize the dynamic simulation. A fully implicit framework is proposed based on the discrete differential geometry (DDG) theory. The equilibrium configuration of a target object is derived by adding damping force into the system, known as the dynamic relaxation method. The mechanical response of a single suspended cable is investigated and compared with the analytical solution for cross-validation. A more intricate scenario is further discussed in detail, where a structure consisting of multiple slender cables is connected through joints. Utilizing the robustness and efficiency of our …