The design of thin structures must take into account the overall instability and the instability of component plates in the form of local buckling. The present paper deals with a non-linear analysis of stability and load carrying capacity for a sheet-metal section with trapezoidal repeating elements when the distortional deformations are taken into account. The plates are assumed to be simply supported at the ends. The investigation is concerned with the stability of thin-walled structures based on the second order non-linear approximation of the asymptotic theory of stability. The asymptotic expansion established by Byskov and Hutchinson (1977) is employed in the numerical calculations performed using the transition matrix method. In the solution obtained, the transformation of buckling modes with an increase in the load up to the ultimate load, the effect of cross-sectional distortions and the shear lag phenomenon are included.