Abstract: Based on the nonlinear geometric relation between strain and displacement of flexible cable, the equilibrium equation under self-weight and influence of temperature are established and an analytical solution of displacement and tension distribution defined in Eulerian coordinate system is accurately obtained. The nonlinear algebraic equations caused by flexible transmission lines with high voltage are solved directly using the modified Powell hybrid algorithm in DNEQNE program. Numerical results from the deformation analysis of flexible transmission lines are presented and compared with the results appeared in recent related literature. The examples demonstrate that the proposed method is more efficient and convenient than others for the nonlinear deformation analysis of flexible cables.