Mild traumatic brain injury caused by blast exposure from Improvised Explosive Devices has become increasingly prevalent in modern conflicts. To investigate head kinematics and brain tissue response in blast scenarios, two solid hexahedral blast-head models were developed in the sagittal and transverse planes. The models were coupled to an Arbitrary Lagrangian-Eulerian model of the surrounding air to model blast-head interaction, for three blast load cases (5 kg C4 at 3, 3.5 and 4 m). The models were validated using experimental kinematic data, where predicted accelerations were in good agreement with experimental tests, and intracranial pressure traces at four locations in the brain, where the models provided good predictions for frontal, temporal and parietal, but underpredicted pressures at the occipital location. Brain tissue response was investigated for the wide range of constitutive properties available. The models predicted relatively low peak principal brain tissue strains from 0.035 to 0.087; however, strain rates ranged from 225 to 571 s-1. Importantly, these models have allowed us to quantify expected strains and strain rates experienced in brain tissue, which can be used to guide future material characterization. These computationally efficient and predictive models can be used to evaluate protection and mitigation strategies in future analysis.