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The finite element computations have been performed to study the axial compression behavior of thin-walled metallic tubes under quasi-static and dynamic loading conditions. The mild steel tubes of circular and square sections were subjected to impact by a 350 kg drop hammer and a 5.13 kg projectile. The impact velocities of the hammer were 3.63–9.68 m/s and that of the projectile were 30–80 m/s. The circular (diameter 40, 60 and 80 mm) and the square tubes (edge length 31.63, 47.34 and 63.05 mm) had the equivalent cross-sectional area, total length (200 mm), wall thickness (1 mm), mass and material. The effect of the quasi-static and dynamic loading and the geometry was studied on the axial crushing behavior, energy absorption characteristics and the modes of deformation. The three-dimensional numerical simulations were performed on ABAQUS/Explicit finite element code and the constitutive and damage behavior of the mild steel was modelled using the Johnson-Cook constitutive and fracture model. The validation of the constitutive and the computational models was carried out by performing the experiments under dynamic loading on circular tubes (40 and 81 mm diameter) and by simulating the available experiments under quasi-static loading on circular and square tubes. Under the dynamic and quasi-static loadings, the axial shortening of both geometric sections decreased with the increase in the size. The absorbed energy, on the other hand, increased with the increase in the diameter of tube while in case of the square tubes no distinguished effect of the size of tube could be noticed on the absorbed energy. • Quasi-static and dynamic axial compression of circular and square mild steel tubes. • An increase in tube diameter reduced axial shortening and increased absorbed energy. • Increase in square tube cross-section reduced axial shortening without affecting energy. • Axial deformation of circular and square tubes was higher under quasi-static loading. • Energy absorption was higher in circular tube under quasi-static and dynamic loading. [ABSTRACT FROM AUTHOR]