An iterative method for the analysis of damaged structures is presented in the context of the displacement method of finite-elemen t analysis, the damage is defined as the loss of stiffness of the structure. The method consists of first finding the solution of the undamaged structure and then determining the perturbed solution due to the damage by using the first two terms of the Taylor's series expansion of the initial solution. The elastic analysis of the effects of the damage, the elastoplastic analysis of the effects of material yielding, and the estimation of the loss of frequency and mode shape deterioration are the primary topics discussed. A brief discussion of a criterion for convergence of the solution and an empirical definition of the extent of damage is included. Applications of the procedure to an airplane wing structure and a truss are presented. This procedure is more economical, in most cases, than direct analysis of the structure with the damage or the usual piecewise linear analysis to include material nonlinearities.