By means of an explicit nonlinear dynamic finite element computer code LS-DYNA and the plastic kinematic Cowper-Symonds model, the nonlinear dynamic response process of fully clamped cylindrical shell subjected to lateral local impact by a hemispherical-nosed projectile were numerically simulated. The dynamic deformation and failure modes of cylindrical shells under different impact conditions were acquired. The minimum impact speed at which cracks through the thickness of the shell wall were generated, termed the speed for rupture, was studied. The results demonstrate that the failure modes of cylindrical shell relates to circumferential impact oblique angle and impact speed. The local dent, dish-shaped deformation and perfoation will occure. The speed for rupture increases with increasing angle of obliquity. The study can be applied to the engineering prediction of the damage or safety of cylindrical shell under lateral local impact and can provide theory reference for safety design.