The static configuration of stay cable considering self-weight and stretch ability was studied by using the super-thin elastic rod model. The equilibrium equation of super-thin elastic rod in the general sense of stay cable was established. The deflection curve of cable, cable force and cable length corresponding to the equilibrium configuration were discussed in the following three cases. 1) When the bending rigidity was ignored, it degenerated into the equilibrium equation of the stay cable when only considering the elastic tension. At this time, the deflection curve equation was consistent with the existing conclusions.2) When elastic tension was ignored, it degenerated into the equilibrium equation of the cable only considering the bending rigidity. The deflection curve equation added a first-order correction term compared to the case when ignoring the bending rigidity. 3) When both elastic tension and bending rigidity were considered, the approximate deflection curve equation was obtained. Taking Sutong Bridge and a laboratory cable as examples, the static parameters of the stay cables under the above three different conditions were calculated respectively, and the influence of bending rigidity and elastic tension on the geometric configuration of the stay cables under different cable lengths and cable forces were analyzed.