A novel prediction model for the buckling failure load of 304 stainless steel under compression was developed using lead–antimony (Pb–Sb) alloys. The temperature-dependent modulus of elasticity of 304 stainless steel was characterized by changing the Sb concentration of the Pb–Sb alloys from 0 to 15 wt%. Slender Pb–Sb plate columns with a rectangular cross section were fabricated by casting. Buckling tests were performed with Pb–Sb alloys under compression at room temperature and compared with numerical simulations that considered the nonlinearity of the specimen, such as initial bending. Based on the buckling failure load and the modulus of elasticity measurements, the linear relationship between the normalized buckling failure loads and the normalized modulus of elasticity was obtained for both Pb-Sb alloy and 304 stainless steel. The relationship between these two correlations makes it possible to predict the buckling failure load of 304 stainless steel at elevated temperatures up to 1200 °C.