Abstract: Buckling of purlins, supporting standing seam roof, simply supported at both ends and acted by pure moment, is studied by a closed-form solution. The uniform distributed torsional restraint provided by the roof sheeting and the lateral elastic restraint provided by the sag-rod placed at the mid-span are considered. The analytical solutions are found, the threshold stiffness of the sag-rod, at which the buckling mode changes from symmetrical buckling to anti-symmetrical one is observed and developed, and the discussion extended to the effects of many factors such as the cross-sectional profile, span length, torsional restraint, sag-rod's stiffness and the height of the sag-rod connecting point along the web on the buckling moment and threshold stiffness. A simplified formula for the buckling moment is also presented based on the calculations covering almost full ranges of various parameters. The investigation shows that the purlin buckles into only one half-wave no matter how large the uniform distributed torsional restraint is, which differs fundamentally from the buckling of a compressed column on a Winkle foundation where several half waves are possible if the elastic stiffness is large enough.