Assuming axisymmetric buckling and according to the adjacent equilibrium criterion, a buckling critical stress formula of a perfect tank wall is first obtained through analysis of elastic–plastic buckling carried out by J2 plastic flow theory. Furthermore, combining the current tank seismic design standards and the results obtained in this paper, a new critical buckling stress formula of the tank wall is derived after correction for material plasticity by introducing a plasticity influence coefficient. Comparisons between the results obtained and those from the relevant formulas in the design standards of America, Japan, China and Europe are also performed. Our research shows that under interaction of high hydraulic and axial compression, the material properties of the tank wall change rapidly, and the buckling strength of the tank wall also decreases rapidly. The relation between the tank wall buckling critical stress and the hydraulic pressure is similar to Rotter's semi-empirical formula. The results presented in this paper can provide technical support in further protection of large oil storage tanks. These are buckling critical stresses of 5 × 104 m3 oil tank calculated by four standards and formulas obtained in this paper. With the increase of circumferential stress of the tank wall, buckling critical stresses from America, Japan and China standards keep constant, while values calculated by Europe standard and formulas in this paper decrease. This phenomenon is attributed to material plasticity. Display omitted ► We propose a simplified analytic model for large oil storage tank suffered elastic–plastic buckling. ► Elastic-plastic buckling analysis of a large oil storage tank was carried out by incremental theory of plasticity. ► A critical stress calculation formula of tank wall instability considering the correction of material plasticity was derived. ► Buckling strength of the tank wall would decrease rapidly under the interaction of high hydraulic pressure and axial pressure.