Abstract In the paper, dynamic buckling of cylindrical shells under axial impact is simulated by using ANSYS/LS-DYNA and the effect of large deformation is considered. The simulation results show that the radius-to-thickness ratio, constraint condition, impact velocity and material parameters have obvious influence on the axisymmetric and unaxisymmetric dynamic buckling of cylindrical shells. The buckling mode of one end free and the other fixed is axisymmetric when the radius-to-thickness ratio is equal or less than 26, whereas it is unaxisymmetric. A scope of axisymmetric buckling of one end clamped and the other fixed is larger than that of one end free and the other fixed, axisymmetric buckling occurs when the radius-to-thickness ratio is equal or less than 31. When the radius-to-thickness ratio, constraint condition and material parameters are given, the buckling mode is from axisymmetric to unaxisymmetric as impact velocity increases. Under the same conditions, the height of cylindrical shells is a known scope, the scope of axisymmetric buckling increases as the height of cylindrical shells increases. The plastic hardening modulus and yield stress of material also influence on the dynamic buckling of cylindrical shells.