This study analyzes 46 brain and 48 spinal-cord impact experiments. The velocity of brain impact was 2.0-10.0 m/s and displacement, 0.75-5.0 mm (5.3-33% compression) using a controlled pneumatic impact. The velocity of spinal-cord impact was 1.5-6.0 m/s and displacement, 1.25-3.25 mm (25-65% compression). Brain injury varied from cortical contusion, diffuse axonal injury (DAI), to fatalities, and spinal-cord injury from temporary to complete loss of somatosensory-evoked potentials. Logist functions were determined for each injury severity and various biomechanical parameters, VC, C, V, and combinations. Brain and spinal-cord injury is most strongly correlated to VC, the viscous response. The goodness-of-fit was x² = 22.1 R-0.84 and p < 0.0000 for fatal brain injury, x² = 27.5, R = 0.96 and p < 0.0000 for cortical contusion, and x² = 17.7, R = 0.49 and p < 0.0001 for partial recovery of spinal-cord conduction. Neural tissue is viscoelastic, with a rate-dependent tolerance related to energy absorption. VC is a measure of energy absorption by impact deformation and is predictive of neural contusion, DAI, long-duration coma, spinal-cord dysfunction, and death. Tolerances for various severities of neural injury are presented. At the tissue level, VC is the product of strain and strain-rate, ε·dε/dt. The research shows that strain is not a sufficient parameter of neural injury risk, and that the product of strain and strain-rate is a key biomechanical parameter for brain and spinal-cord injury.