Aluminium is one of the traditional structural materials. Structures made of aluminium alloys are widely used in the civil engineering for erection of new civil and industrial buildings and reconstruction of the existing ones. Increased corrosion resistance, stability of mechanical properties at negative temperatures, lightness and increased durability are the main advantages of aluminium alloys as the structural materials. Design approaches described in  EN 1999  and SNiP 2.03.06-85 for the aluminium elements, subjected to bending and combined bending and compression, were compared analytically and on the base of laboratorial experiment for the simple beams with the rectangular hollow cross-sections with the heights 65, 85 and 105 mm loaded by the two concentrated forces. It was stated, that the difference between the results is within the limits from 5.82 % to 12.92 %. The differences between the experimental and numerical results are within the limits from 3 % to 7 % for both methods. Rational values of height of the transversal arch, amount of the arch’s segments and a spacing of transversal arches of load-bearing framework for spacious exterior structure were determined by the response surface method for the structure with the span equal to 9 m. It was shown, that the rational height of the transversal arch and amount of the arch’s segments changes from 1.76 to 1.94 m and from 10.70 to 11.97 m, correspondingly. The corresponding minimum materials consumptions were equal to 6.16, 5.38 and 5.54 kg/m2.