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The subject of the analysis are thin-walled aluminum boxes connected by mechanical fasteners only or with the addition of cohesive layer. The analyzed elements have a great potential in the construction of aircraft engines as well as in other applications where thin-walled components are used. Cohesive connections, are now increasingly used in construction of structural components. Therefore, this paper presents results and comparison of selected thin-walled structure connected with mechanical connectors and cohesive layers. The main objective in this paper was to perform FEM analysis and to determine mechanical response of the selected thin-walled structure with different types of connections under quasi-static load. Aluminum boxes were subjected to a complex load, such as bending and twisting. The numerical model includes 2 damage processes in the: (1) aluminum, and (2) fasteners. This allowed us to determine locations of the most stressed, and most exposed to damage areas inside of the whole thin-walled box. The obtained results also allow to determine degree of usefulness of cohesive joints in the construction of the thin-walled structures under influence of quasi-static loads.