This article presents analytical studies of the stability and strength of thin-walled beams with non-standard cross-sectional geometry, manufactured by Zaprom Ltd. The analyses cover four load conditions, for which critical buckling load values were determined. The studies were conducted for three example beams made of innovative profiles designed to improve structural performance. The paper utilizes an approach combining theory based on the principle of conservation of potential energy with numerical analysis using the finite-stripe method (FSM). The results allow for an assessment of the influence of loading conditions and geometric parameters on the forms of instability and critical load values. The analyses provide a basis for further optimization of the thin-walled profile shapes, taking into account both load-bearing efficiency and structural safety.