The TCUD method (Kim and Lee, 2001) can minimize undesirable lateral displacements in cable bridge structures by including the unstrained lengths of the cable members as unknowns and introducing additional constraint conditions. The axial deformations in the girder and the main tower deviating from the target configuration are, however, unavoidable when self-anchored cable bridges are considered. On the other hand, the IFM (initial force method) can be used to adjust the axial deformations to conform to the initial shape but it is critical that the unstrained lengths of the cables are accurately evaluated. In this study, improved schemes for the TCUD method and the IFM for finding the initial shape of 3 dimensional cable-supported bridges under dead load, are presented. For this purpose, the TCUD method and the initial force method are firstly reviewed. Two improved algorithms, which can overcome shortcomings of the previous initial-shaping analysis methods, are developed based on an elastic catenary cable element and a nonlinear space frame element. Finally, the accuracy and effectiveness of the proposed analysis algorithms are demonstrated through the numerical application to 3 dimensional initial shape problems for self-anchored suspension and cable-stayed bridges.