In this dissertation, theoretical, computational, and experimental methodologies are introduced to determine the rate-dependent material properties of the brain tissue. Experiments have shown that the brain tissue is significantly rate-dependent. To examine the range of strain rates at which trauma might happen, a validated finite element (FE) human head model was initially employed to examine the biomechanics and dynamic behavior of the head and brain under impact and blast loads. The strain rates to cause traumatic brain injury (TBI) were found to be in the range of 36 to 241 1/s, under these types of loadings. These findings provided a good estimation prior to exploring the required experiments for characterizing the brain tissue. The brain samples were tested by employing unconfined compression tests at three different deformation rates of 10 (n= 10 brain samples), 100 (n=8), and 1000 mm/sec (n=12). It was found that the tissue exhibited a significant rate-dependent behavior with various compression rates. Two different material characterization approaches were proposed to evaluate the rate-dependent mechanical responses of the brain. In the first approach, based on the parallel rheological framework, a single-phase viscoelastic model which captures the key aspects of the rate-dependency in large strain behavior was introduced. The extracted material parameters showed an excellent constitutive representation of tissue response in comparison with the experimental test results (R^2=0.999). The obtained material parameters were employed in the FE simulations of the brain tissue and successfully verified by the experimental results. In the second approach, the brain tissue is modeled as a biphasic continuum, consisting of a compressible solid matrix fully saturated with an incompressible interstitial fluid. The governing equations based on conservation of mass and momentum are used to describe the solid-fluid interactions. This viscoelastic biphasic model can effectively estimate the rate-dependent tissue deformations, the hydrostatic pressure as well as fluid diffusion through the tissue. Although both single-phasic, as well as bi-phasic models, can successfully capture the key aspects of the rate-dependency in large strain deformation, it was shown the biphasic model can demystify more phenomenological behavior of this tissue that could not be perceived with yet established, single-phasic approaches.