The objective of this study was to analyze the elastic critical local buckling of cold-formed lipped channel sections using the energy method. A mechanical model and unique displacement functions simulating the local buckling behavior were proposed to consider the plate element interaction. Using the proposed mechanical mode, an analytical formula for local buckling that directly reflects the parameters of the channel member was proposed. Based on the proposed formula, the relationship between the cross-sectional geometry and local buckling behavior was investigated. In addition, a simplified design equation was proposed. The reliability and effectiveness of the proposed equations were presented by comparing with the results of eigenvalue analysis based on the finite element method.