Composite materials are mostly used in applications where stiffness-to-weight or strength-to-weight ratios are critical. For example, there can be produced a large number of acceptable designs that support a specific loading condition by varying fibre orientation in each ply, or in a certain number of plies. Due to ease of construction, structural elements, such as box structures, are widely used as a load bearing member in the fields of civil, mechanical and aeronautical engineering. The paper presents an analysis of finite element stability of a thin-walled structure which can be used in civil constructions. The structure is made of FRP composite material. The structure is stiffened with ribs which are made of the same composite, steel and aluminum. The critical buckling pressure was determined for this structure. The advantage of using FRP and sandwich composite, compared to conventional materials as steel or aluminum, consists in high strength to weight ratios, high corrosion resistance, lightweight and excellent fatigue performance. A neural network model was created and used for the prediction of stability behavior of the analyzed elements.