Traumatic brain injury is a major cause of morbidity in civilian as well as military populations. Computational simulations of injurious events are an important tool to understanding the biomechanics of brain injury and evaluating injury criteria and safety measures. However, these computational models are highly dependent on the material parameters used to represent the brain tissue. Reported material properties of tissue from the cerebrum and cerebellum remain poorly defined at high rates and with respect to anisotropy. In this work, brain tissue from the cerebrum and cerebellum of male Göttingen minipigs was tested in one of three directions relative to axon fibers in oscillatory simple shear over a large range of strain rates from 0.025 to 250s-1. Brain tissue showed significant direction dependence in both regions, each with a single preferred loading direction. The tissue also showed strong rate dependence over the full range of rates considered. Transversely isotropic hyper-viscoelastic constitutive models were fit to experimental data using dynamic inverse finite element models to account for wave propagation observed at high strain rates. The fit constitutive models predicted the response in all directions well at rates below 100s-1, after which they adequately predicted the initial two loading cycles, with the exception of the 250s-1 rate, where models performed poorly. These constitutive models can be readily implemented in finite element packages and are suitable for simulation of both conventional and blast injury in porcine, especially Göttingen minipig, models.