The transient response to longitudinal impact of flexible rods with Hertz contact is closely related to the extent of deformations with different impact parameters. By means of LS-DYNA, for different radius and different speeds, the longitudinal impact of a hammer with a rounded end on a drill rod is numerically simulated in this article. Simulations demonstrate that there is an obvious dif-ference between analytical solution and numerical solution on condition of short curvature radius. In the circumstance contact pressure increases, the boundary of the yield zone exceeds that of the contact zone, and the significant plastic deformation reduces the intensity of contact pressure pulse. Contact force-time curves in loading and unloading phases shift down. The numerical solution is in good agree-ment with analytical solution on condition of large curvature radius and impact speeds. The deforma-tion of yield region is constrained by the surrounding elastic region and no significant plastic deforma-tion appears.