The current study investigates the stability and failure analysis of thin-walled composite columns with a top-hat and channel cross section, subjected to axial compression. The analyzed structures were made of composite material (carbon fiber reinforced polymer) by autoclave technique. The study included experimental tests on actual specimens and numerical simulations on numerical models using finite element method (in ABAQUS® program).Experimental-numerical analysis was conducted over the full range of loading (until failure phenomenon). Regarding the experimental tests, postbuckling equilibrium paths as well as acoustic emission signals were registered, which directly allowed for comprehensive analysis of failure phenomenon of composite material. In case of numerical simulations, two independent numerical damage models were used. The first one constitutes the progressive failure analysis, considering the damage initiation criteria using Hashin's theory and damage evolution based on the energy criterion. The second one constitutes the cohesive zone model, which was used to simulate failure of composite material caused by delamination phenomenon. Both experimental and numerical results show high agreement. Furthermore, the obtained results reveal an interesting relationship between buckling, postbuckling, and failure phenomenon of the analyzed structures.