In this paper, the phenomenon of stability and failure of axially compressed thin-walled structures with central cut-out, made of composite materials, were investigated. The tested structures were made of carbon-epoxy composite material, using autoclave technique. Within the framework of the studies, experimental tests on actual constructions were carried out, as well as advanced numerical simulations using the finite element method in the ABAQUS® software. The process of axial compression of thin-walled composite structures was carried out in the full range of load, up to total failure. During the experimental tests, post-critical equilibrium paths were recorded, using the universal testing machine - Instron 4485. Additionally, acoustic emission signals were recorded using the AMSY-5 device, and the level of deformation was tested, using the non-contact three-dimensional measurement technique offered by the ARAMIS system. Simultaneously to the experimental tests, numerical calculations were carried out using progressive failure analysis (PFA), based on the damage initiation Hashin's criterion of as well as damage evolution based on the energy criterion. In the numerical analyses, the cohesive zone model (CZM) and the model allowing for the simulation of damage due to material cracking (xFEM) were also used. A significant effect of conducted numerical calculations was the simulation of the failure phenomenon of thin-walled composite structures, in terms of loss of load-carrying capacity, using three independent damage models (model PFA, CZM and xFEM). The above constitutes a novelty, with respect to current papers from the subject literature. The use of the above-mentioned techniques of experimental research and numerical simulations made it possible to conduct a comprehensive analysis of the damage state of the composite material. The obtained results of the numerical tests demonstrated very high agreement with the results of the experimental studies.