This paper introduces algorithms for computer-aided calculation, based on a proposed computational model for stay cables, decomposed from a bridge’s structural system. These algorithms determine the necessary tension forces and corresponding deformations in the cables for individual strand tensioning using lightweight hydraulic jacks. Two tensioning methods are discussed: the first involves single-cycle tensioning with varying force intensities, while the second employs multiple cycles by applying forces of constant intensity until achieving an equalization of forces in all strands of the cable. The efficiency of the proposed procedures is demonstrated through a numerical example.