This paper develops energy-based equations for symmetric distortional buckling in columns with Zed and rack sections. Using the Rayleigh quotient method, two sets of displacement functions are assumed for each cross-section type and closed-form expressions depending on geometrical parameters of the cross-sections are obtained for critical length and buckling stress. Additionally the proposed deformed shapes allow a closed-form derivation of the warping profile of the cross-sections. A parametric study is conducted to compare the derived expressions to GBTUL numerical results for a wide range of cross-section geometries. The average results σcr,proposed/σcr,GBTUL of the study are 0.995 ± 0.005 for Zed sections and 0.988 ± 0.025 for rack sections. Therefore the proposed equations may be applied in practical design of axially compressed thin-walled cold-formed members as an alternative to computational tools.