In this paper, the stressing state modeling analysis of the residual strain data of H-steel columns reveals three characteristic points that exist during the failure of H-steel columns. Also, the correctness of the stressing state analysis method, residual, and buckling characteristic pairs was verified. First, the experimental residual strains were transformed into generalized strain energy density (GSED) values as the state variables for establishing the stressing state mode and characteristic parameters (characteristic pairs). The Mann-Kendall (M-K) criterion is applied to the normalized GSED sum-j curves to reveal the characteristic points P, Q, and U of the evolving stressing state of the H-steel column. Characteristic point P is defined as the elastic-plastic branch point of the H-steel column, characteristic point Q is defined as the failure starting point, and characteristic point U is defined as the progressive failure point. Around the characteristic points of the H-steel columns, the directly modeled stressing state characteristic pairs, residual characteristic pairs, and buckling characteristic pairs produce significant mutation characteristics. This phenomenon verifies the correctness of the revealed H-steel column characteristic points and the rationality of this paper's stressing state modeling method. Then, it is proposed that the elastic-plastic branch point P can be directly used as the design reference point, and it is compared with the design point given by Code EN1993–1–5. In conclusion, this paper provides new ideas for analyzing steel structures and opens up the value of residual strain data in structural analysis. •Present the new theoretical basis to reveal the essential working behavior of H-steel columns.•Propose the methods modeling the stressing states of H-steel columns using residual strains.•Find the starting point of the H-steel column’s failure process complying with the natural law.•Reveal the elasto-plastic branch feature which would be the design principle for H-steel columns.•Explore the new application of experimental strain data in structural analysis and design.