Experimental analysis of buckling stress for box-shaped beams with non-linear walls was performed. Calculations in Ansys showed that the critical stresses of local buckling of beams with non-linear walls are higher than in beams with standard walls. The value of critical stresses of local buckling grows nonlinearly with increasing wall curvature. Dependences are obtained for estimating the critical stresses of local buckling based on the results of a numerical experiment with varying geometric parameters of the beam. For experimental verification of the obtained dependences, a test facility was developed. It allows determining the forces, deformations, and stresses in area where the local buckling of box-shaped beams is lost. A comparative experiment and calculation of beams with linear and non-linear walls showed that non-linear walls in box-shaped beams have a higher (by 2.5–4 times) critical stress value than standard linear walls.