The necessity for considering both strength criteria and postbuckling effects in calculating the load-carrying capacity in compression of thin-wall composite structures with impact damage is substantiated. An original applied method ensuring solution of these problems with an accuracy sufficient for practical design tasks is developed. The main advantage of the method is its applicability in terms of computing resources and the set of initial data required. The results of application of the method to solution of the problem of compression of fragments of thin-wall honeycomb panel damaged by impacts of various energies are presented. After a comparison of calculation results with experimental data, a working algorithm for calculating the reduction in the load-carrying capacity of a composite object with impact damage is adopted.