Abstract: A theoretical analysis and cable force identification algorithm for large-span suspension cable structures, considering elastic support boundaries, are proposed in this paper. First, a partial differential equation for the vertical vibration of the suspension cable is established based on mechanical analysis. Elastic boundary conditions are incorporated, and the modal functions of the cable are expressed as superposition of trigonometric series satisfying these conditions. An incremental formula for horizontal cable forces is derived and substituted into the frequency equation to determine the vibration frequencies and modal functions. An iterative algorithm for calculating the tensile forces of suspension cables with elastic supports, based on known frequencies, is then introduced. Results show that new frequencies and modes are introduced by elastic boundaries and existing frequencies are significantly affected, while existing modes are minimally impacted. Further parametric analysis reveals that symmetric frequencies are more sensitive to boundary support stiffness compared to antisymmetric frequencies. For inclined cables with unequal end heights, the vertical support stiffness at the lower end has a minimal effect on symmetric frequencies. The proposed cable force identification algorithm, considering elastic boundary effects, accurately back-calculates cable forces from known structural frequencies, whereas ignoring elastic supports leads to substantial discrepancies between the calculated and actual forces, demonstrating the algorithm's effectiveness and practicality.