Nonlinear behavior in structures is frequently encountered in practice, and poses considerable difficulties in the numerical solution of the governing equations. Iteration is the most powerful technique available for solving such problems. A technique is presented which enables iteration routines to be classified from the standpoint of their convergence characteristics. This is then compared with several other methods of solving nonlinear structures, and the reason why some behave better than others is deduced. The derivation and application of a powerful numerical tool has been devised, which is applied to the solution of a suspended cable truss. The results are compared with those obtained from a model truss experiment.