Using the principles of continuum mechanics, the general, incremental, geometrically nonlinear, equilibrium equations for the displacement-based finite element method are derived in both the Total Lagrangian and Updated Lagrangian form. The Updated Lagrangian equations are then specialized for the analysis of three-dimensional cable structures. Two node and three node isoparametric finite elements are derived and a program is developed which implements both elements. Comparisons between the two elements are made to determine their relative merits. In addition, four separate iterative solution techniques are investigated in the solution of the equilibrium equations: the Newton-Raphson method, the Modified Riks-Wempner method, an Orthogonal Trajectory Accession method, and a Dynamic Relaxation approach. An extension of this investigation is a comparison between the Riks-Wempner method and Orthogonal Trajectory Accession. / M.S.