Based on the nonlinear geometric relation between strain and displacement for flexible cable, the equilibrium equation under self-weight and influence of temperature was established and an analytical solution of displacement and
tension distribution defined in Eulerian coordinate system was accurately obtained. The nonlinear algebraic equations caused by cable structure were solved directly using the modified Powell hybrid algorithm with high precision routine DNEQNE of Fortran. For example, a cable structure consisting of three cables jointly supported by a vertical spring and all the other ends fixed was calculated and compared with various methods by other scholars.