The dynamic behavior of porcine brain tissue, obtained from a series of in vitro observations and experiments, is analyzed and described here with the aid of a large strain, nonlinear, viscoelastic constitutive model. Mixed gray and white matter samples excised from the superior cortex were tested in unconfined uniaxial compression within 15 h post mortem. The test sequence consisted of three successive load–unload segments at strain rates of 1, 0.1 and 0.01 s⁻¹, followed by stress relaxation (n = 25). The volumetric compliance of the tissue was assessed for a subset of specimens (n = 7) using video extensometry techniques. The tissue response exhibited moderate compressibility, substantial nonlinearity, hysteresis, conditioning and rate dependence. A large strain kinematics nonlinear viscoelastic model was developed to account for the essential features of the tissue response over the entire deformation history. The corresponding material parameters were obtained by fitting the model to the measured conditioned response (axial and volumetric) via a numerical optimization scheme. The model successfully captures the observed complexities of the material response in loading, unloading and relaxation over the entire range of strain rates. The accuracy of the model was further verified by comparing model predictions with the tissue response in unconfined compression at higher strain rate (10 s⁻¹) and with literature data in uniaxial tension. The proposed constitutive framework was also found to be adequate to model the loading response of brain tissue in uniaxial compression over a wider range of strain rates (0.01–3000 s⁻¹), thereby providing a valuable tool for simulations of dynamic transients (impact, blast/shock wave propagation) leading to traumatic brain injury.