SummaryThe problem discussed is that of the elastic local instability of a uniformly compressed thin-walled strut composed of a number of flat component plates. The strut is essentially “ open ” in cross-sectional form, while reinforcing flanges are attached to the extreme edges. An overall stability equation, based on the small deflection theory of plate bending, is derived from the conditions which must hold at the common and extreme longitudinal edges of the strut.It is shown that the critical compression stress induces a mode of buckling which involves a whole number of sinusoidal half-waves in the longitudinal direction. Furthermore, the number of half-waves is common to all component plates of the strut. The general’ stability equation—a zero determinant of high order—lends itself to expansion in terms of 4th order minors, which may again be expressed in terms of seven basic functions. A knowledge of these functions is sufficient for the solution of any problem, however complex, within the scope of the general analysis.Application of the basic functions to the solution of three different problems yields results which indicate the need for considerable care in the design of thin-walled struts with reinforcing flanges. In struts of this type a longer wavelength of buckling is possible than is commonly associated with local instability problems.