We use computational simulations to compare the impact response of different football and U.S. Army helmet pad materials. We conduct experiments to characterise the material response of different helmet pads. We simulate experimental helmet impact tests performed by the U.S. Army to validate our methods. We then simulate a cylindrical impactor striking different pads. The acceleration history of the impactor is used to calculate the head injury criterion for each pad. We conduct sensitivity studies exploring the effects of pad composition, geometry and material stiffness. We find that (1) the football pad materials do not outperform the currently used military pad material in militarily relevant impact scenarios; (2) optimal material properties for a pad depend on impact energy and (3) thicker pads perform better at all velocities. Although we considered only the isolated response of pad materials, not entire helmet systems, our analysis suggests that by using larger helmet shells with correspondingly thicker pads, impact-induced traumatic brain injury may be reduced.