Based on the basic stretch- draw principle of parallel strand stay cables,formulas respectively describingthe configuration of target state and the unstressed cable length were set up according to the catenary theory.Then,two problems existing in the stretch- draw process of parallel strand stay cables were put forward,and the corre-sponding solving methods were proposed and a calculation program was compiled with Matlab to determine the sin-gle strand initial tension.Finally,a case study on the Tongling rail- road cable- stayed bridge under construction wasconducted.The results show that the proposed method is effective and reliable,and that it may provide theoreticalreferences for the construction of parallel strand stay cables.