A nonlinear finite element procedure for cable system analysis is presented in this paper. Both geometrical and material nonlinearities are taken into account. The nonlinear stress‐strain relationship proposed by Jonatowski and Birnstiel is adopted for describing the elasto‐plastic behavior of cable material. The ultimate carrying capacity and inelastic structural behavior of several cable systems are examined in this study. Conditions of loading, unloading and reloading, slackness and rupture of cable are also discussed. For nonlinear computation, the Newton‐Raphson method is utilized. A stable, fast computation algorithm with two iteration loops (elastic solution loop and material loop) is set up for large displacement elasto‐plastic analysis of cable systems. Numerical results show good agreement with previous studies.