WH E N THE SURFACE of a multicellular supersonic wing is heated by the air flowing in the boundary layer (see Fig. 1), the temperature of the cover plates rises and the cover plates expand. This expansion is resisted by the shear webs which remain comparatively cool as they are not in contact with the boundary layer and are heated only by the cover plates through conduction and possibly through convection and radiation. T h e resistance of the shear webs sets up compressive stresses in the cover plates and tensile stresses in the shear webs. Under the compressive stresses so arising, the cover plates have been observed to buckle. Buckling of the cover plates is objectionable not only for structural reasons bu t also because the buckled, wavy surfaces alter the flow of air, lead to losses in aerodynamic efficiency, and may even cause aerodynamic disturbances resulting in failure. I t is important , therefore, for the airplane designer to be able to predict the onset of thermal buckling—that is, buckling caused by stresses arising from a nonuniform heating of the structure. In multicellular wing structures, the variation of the temperature through the thickness of the cover plates is usually not pronounced, a t least not when the speed of flight does not exceed Mach Numbers of 3 or 4. Similarly, with a wing of normal aspect ratio, the variation in the spanwise direction may be disregarded in order to simplify the analysis. However, the heating rate generally varies noticeably in the chordwise direction and with time. As all possible variations in flight pa th and construction cannot be considered simultaneously when formulas to be used in practical work are developed, i t is assumed in the present analysis that , over one cell of the wing and during the period of time considered, the heat inpu t q from the air to the cover plates is constant. In an actual problem when q is a variable, substitution of its average value into the formulas here derived should give an indication of the danger of buckling. Hea t transfer from cover plate to web through the interior of