Combat helmets are expected to protect the warfighter from a variety of blunt, blast, and ballistic threats. Their blunt impact performance is evaluated by measuring linear headform acceleration in drop tower tests, which may be indicative of skull fracture, but not necessarily brain injury. The current study leverages a blunt impact biomechanics model consisting of a head, neck, and helmet with a suspension system to predict how pad stiffness affects both (1) linear acceleration alone and (2) brain tissue response induced by both linear and rotational acceleration. The approach leverages diffusion tensor imaging information to estimate how pad stiffness influences white matter tissue strains, which may be representative of diffuse axonal injury. Simulation results demonstrate that a softer pad material reduces linear head accelerations for mild and moderate impact velocities, but a stiffer pad design minimizes linear head accelerations at high velocities. Conversely, white matter tract-oriented strains were found to be smallest with the softer pads at the severe impact velocity. The results demonstrate that the current helmet blunt impact testing standards' standalone measurement of linear acceleration does not always convey how the brain tissue responds to changes in helmet design. Consequently, future helmet testing should consider the brain's mechanical response when evaluating new designs.